This is pdfeTeX, Version 3.141592-1.30.4-2.2 (Web2C 7.5.5) (format=pdflatex 2005.11.9)  28 FEB 2006 17:49
entering extended mode
**manual
(./manual.tex
LaTeX2e <2003/12/01>
Babel <v3.8d> and hyphenation patterns for american, french, german, ngerman, d
utch, italian, norsk, portuges, spanish, swedish, nohyphenation, loaded.
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/report.cls
Document Class: report 2004/02/16 v1.4f Standard LaTeX document class
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/size11.clo
File: size11.clo 2004/02/16 v1.4f Standard LaTeX file (size option)
)
\c@part=\count79
\c@chapter=\count80
\c@section=\count81
\c@subsection=\count82
\c@subsubsection=\count83
\c@paragraph=\count84
\c@subparagraph=\count85
\c@figure=\count86
\c@table=\count87
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/a4wide/a4wide.sty
Package: a4wide 1994/08/30

(/usr/local/teTeX/share/texmf.tetex/tex/latex/ntgclass/a4.sty
Package: a4 2004/04/15 v1.2g A4 based page layout
))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2002/01/22 v2.2d

(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amsfonts.sty
Package: amsfonts 2001/10/25 v2.2f
\@emptytoks=\toks14
\symAMSa=\mathgroup4
\symAMSb=\mathgroup5
LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
(Font)                  U/euf/m/n --> U/euf/b/n on input line 132.
))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/inputenc.sty
Package: inputenc 2004/02/05 v1.0d Input encoding file

(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/latin1.def
File: latin1.def 2004/02/05 v1.0d Input encoding file
))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/makeidx.sty
Package: makeidx 2000/03/29 v1.0m Standard LaTeX package
)
\@indexfile=\write3
\openout3 = `manual.idx'.


Writing index file manual.idx
(/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/color.sty
Package: color 1999/02/16 v1.0i Standard LaTeX Color (DPC)

(/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/color.cfg
File: color.cfg 2005/02/03 v1.3 color configuration of teTeX/TeXLive
)
Package color Info: Driver file: pdftex.def on input line 125.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/pdftex.def
File: pdftex.def 2002/06/19 v0.03k graphics/color for pdftex
\Gread@gobject=\count88
))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/fancyvrb/fancyvrb.sty
Package: fancyvrb 1998/07/17

Style option: `fancyvrb' v2.6, with DG/SPQR fixes <1998/07/17> (tvz)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/keyval.sty
Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
\KV@toks@=\toks15
)
\FV@CodeLineNo=\count89
\FV@InFile=\read1
\FV@TabBox=\box26
\c@FancyVerbLine=\count90
\FV@StepNumber=\count91
\FV@OutFile=\write4

No file fancyvrb.cfg.
) (/usr/local/teTeX/share/texmf.tetex/tex/latex/pslatex/pslatex.sty
Package: pslatex 1996/07/24 v1.2 pslatex emulation (DPC)
LaTeX Font Info:    Redeclaring symbol font `operators' on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `normal'
(Font)                  OT1/cmr/m/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Redeclaring symbol font `letters' on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `normal'
(Font)                  OML/cmm/m/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `bold'
(Font)                  OML/cmm/b/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Redeclaring symbol font `symbols' on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `normal'
(Font)                  OMS/cmsy/m/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `bold'
(Font)                  OMS/cmsy/b/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Redeclaring symbol font `largesymbols' on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `normal'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `bold'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
\symbold=\mathgroup6
\symitalic=\mathgroup7
LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `normal'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Redeclaring math alphabet \mathit on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `normal'
(Font)                  OT1/cmr/m/it --> OT1/ptm/m/it on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
(Font)                  OT1/cmr/bx/it --> OT1/ptm/m/it on input line 75.
)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/hyperref.sty
Package: hyperref 2003/11/30 v6.74m Hypertext links for LaTeX
\@linkdim=\dimen103
\Hy@linkcounter=\count92
\Hy@pagecounter=\count93

(/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/pd1enc.def
File: pd1enc.def 2003/11/30 v6.74m Hyperref: PDFDocEncoding definition (HO)
)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/hyperref.cfg
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive and teTeX
)
Package hyperref Info: Option `bookmarks' set `false' on input line 1830.
Package hyperref Info: Option `colorlinks' set `true' on input line 1830.
Package hyperref Info: Option `breaklinks' set `true' on input line 1830.
Package hyperref Info: Hyper figures OFF on input line 1880.
Package hyperref Info: Link nesting OFF on input line 1885.
Package hyperref Info: Hyper index ON on input line 1888.
Package hyperref Info: Plain pages ON on input line 1893.
Package hyperref Info: Backreferencing ON on input line 1898.

Implicit mode ON; LaTeX internals redefined
Package hyperref Info: Bookmarks OFF on input line 2010.
(/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/backref.sty
Package: backref 2003/03/20 v1.23 Bibliographical back referencing
)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/url/url.sty
\Urlmuskip=\muskip10
Package: url 2004/03/15  ver 3.1  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 2143.
\Fld@menulength=\count94
\Field@Width=\dimen104
\Fld@charsize=\dimen105
\Choice@toks=\toks16
\Field@toks=\toks17
Package hyperref Info: Hyper figures OFF on input line 2618.
Package hyperref Info: Link nesting OFF on input line 2623.
Package hyperref Info: Hyper index ON on input line 2626.
Package hyperref Info: backreferencing ON on input line 2631.
Package hyperref Info: Link coloring ON on input line 2636.
\c@Item=\count95
\c@Hfootnote=\count96
)
*hyperref using default driver hpdftex*
(/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/hpdftex.def
File: hpdftex.def 2003/11/30 v6.74m Hyperref driver for pdfTeX

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/pifont.sty
Package: pifont 2004/09/15 PSNFSS-v9.2 Pi font support (SPQR) 
LaTeX Font Info:    Try loading font information for U+pzd on input line 63.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/upzd.fd
File: upzd.fd 2001/06/04 font definitions for U/pzd.
)
LaTeX Font Info:    Try loading font information for U+psy on input line 64.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/upsy.fd
File: upsy.fd 2001/06/04 font definitions for U/psy.
))
\Fld@listcount=\count97
\@outlinefile=\write5
)
\pagenrlog=\write6
\openout6 = `manual.pnr'.

\backslashbox=\box27
 (./manual.aux

LaTeX Warning: Label `Involution' multiply defined.


LaTeX Warning: Label `IsUnit' multiply defined.


LaTeX Warning: Label `LeftIdealBySubgroup' multiply defined.


LaTeX Warning: Label `Embedding' multiply defined.


LaTeX Warning: Label `LieUpperCodimensionSeries' multiply defined.

)
\openout1 = `manual.aux'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 50.
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 50.
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 50.
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for OMS/pzccm/m/n on input line 50.
LaTeX Font Info:    Try loading font information for OMS+pzccm on input line 50
.
 (/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/omspzccm.fd
File: omspzccm.fd 2000/01/03 Fontinst v1.801 font definitions for OMS/pzccm.
)
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 50.
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 50.
LaTeX Font Info:    ... okay on input line 50.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 50.
LaTeX Font Info:    ... okay on input line 50.

(/usr/local/teTeX/share/texmf.local/tex/context/base/supp-pdf.tex
(/usr/local/teTeX/share/texmf.local/tex/context/base/supp-mis.tex
loading : Context Support Macros / Miscellaneous (2004.10.26)
\protectiondepth=\count98
\scratchcounter=\count99
\scratchtoks=\toks18
\scratchdimen=\dimen106
\scratchskip=\skip43
\scratchmuskip=\muskip11
\scratchbox=\box28
\scratchread=\read2
\scratchwrite=\write7
\zeropoint=\dimen107
\onepoint=\dimen108
\onebasepoint=\dimen109
\minusone=\count100
\thousandpoint=\dimen110
\onerealpoint=\dimen111
\emptytoks=\toks19
\nextbox=\box29
\nextdepth=\dimen112
\everyline=\toks20
\!!counta=\count101
\!!countb=\count102
\recursecounter=\count103
)
loading : Context Support Macros / PDF (2004.03.26)
\nofMPsegments=\count104
\nofMParguments=\count105
\MPscratchCnt=\count106
\MPscratchDim=\dimen113
\MPnumerator=\count107
\everyMPtoPDFconversion=\toks21
)
Package hyperref Info: Link coloring ON on input line 50.
 (/usr/local/teTeX/share/texmf.tetex/tex/latex/hyperref/nameref.sty
Package: nameref 2003/12/03 v2.21 Cross-referencing by name of section
\c@section@level=\count108
)
LaTeX Info: Redefining \ref on input line 50.
LaTeX Info: Redefining \pageref on input line 50.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <24.88> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 54.
LaTeX Font Info:    Font shape `OT1/phv/bx/n' in size <24.88> not available
(Font)              Font shape `OT1/phv/b/n' tried instead on input line 54.
LaTeX Font Info:    Font shape `OT1/phv/b/n' will be
(Font)              scaled to size 22.39185pt on input line 54.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <14.4> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 56.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <12> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 60.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 68.

Underfull \hbox (badness 10000) in paragraph at lines 66--99

 []

[1

{/usr/local/teTeX/share/texmf.local/fonts/map/pdftex/updmap/pdftex.map}]
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 8.99994pt on input line 105.
LaTeX Font Info:    Try loading font information for OT1+ptmcm on input line 11
1.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/ot1ptmcm.fd
File: ot1ptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OT1/ptmcm.
)
LaTeX Font Info:    Try loading font information for OML+ptmcm on input line 11
1.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/omlptmcm.fd
File: omlptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OML/ptmcm.
)
LaTeX Font Info:    Try loading font information for OMX+psycm on input line 11
1.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/omxpsycm.fd
File: omxpsycm.fd 2000/01/03 Fontinst v1.801 font definitions for OMX/psycm.
)
LaTeX Font Info:    Try loading font information for U+msa on input line 111.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Try loading font information for U+msb on input line 111.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <7.4> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 111.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <6> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 111.


! LaTeX Error: There's no line here to end.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.113  }\\[1cm]
               
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

LaTeX Font Info:    Font shape `OMS/ptm/m/n' in size <10> not available
(Font)              Font shape `OMS/pzccm/m/n' tried instead on input line 117.


Underfull \hbox (badness 10000) in paragraph at lines 126--128

 []


! LaTeX Error: There's no line here to end.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.148  }\\[1cm]
               
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

LaTeX Font Info:    Font shape `OT1/phv/m/sl' will be
(Font)              scaled to size 7.19995pt on input line 149.
[2] (./manual.toc
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 1.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <8> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 2.
LaTeX Font Info:    Font shape `OT1/phv/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/phv/b/n' tried instead on input line 7.
LaTeX Font Info:    Font shape `OT1/phv/b/n' will be
(Font)              scaled to size 9.85492pt on input line 7.
 [3

] [4])
\tf@toc=\write8
\openout8 = `manual.toc'.

 [5]
Chapter 1.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <20.74> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 157.
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 9.85492pt on input line 164.
[6

]
Underfull \hbox (badness 2903) in paragraph at lines 216--217
[]\OT1/ptm/m/n/10.95 To use the \OT1/phv/m/n/10.95 LA-GUNA \OT1/ptm/m/n/10.95 o
n-line help it is nec-es-sary to in-stall the \OT1/phv/m/n/10.95 GAP\OT1/ptm/m/
n/10.95 4 pack-age \OT1/phv/m/n/10.95 GAP-
 []


Underfull \hbox (badness 3861) in paragraph at lines 218--219
[]\OT1/phv/m/n/10.95 LAGUNA \OT1/ptm/m/n/10.95 is dis-tributed in stan-dard for
-mats (\OT1/pcr/m/n/10.95 zoo\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 tar.gz\OT1
/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 tar.bz2\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10
.95 -win.zip\OT1/ptm/m/n/10.95 ) and
 []


Underfull \hbox (badness 1248) in paragraph at lines 218--219
\OT1/ptm/m/n/10.95 can be ob-tained from [][]\OT1/pcr/m/n/10.95 http://ukrgap.e
xponenta.ru/laguna.htm[][]\OT1/ptm/m/n/10.95 . To un-pack the archive
 []

[7]
Chapter 2.
[8

] [9] [10] [11] [12] [13]
Chapter 3.
[14

]

LaTeX Warning: Command \textless invalid in math mode on input line 532.

LaTeX Font Info:    Try loading font information for OML+ptm on input line 532.

(/usr/local/teTeX/share/texmf.tetex/tex/latex/psnfss/omlptm.fd
File: omlptm.fd 
)
LaTeX Font Info:    Font shape `OML/ptm/m/n' in size <10.95> not available
(Font)              Font shape `OML/cmm/m/it' tried instead on input line 532.


LaTeX Warning: Command \textless invalid in math mode on input line 532.

[15]
Underfull \hbox (badness 10000) in paragraph at lines 594--598
\OT1/ptm/m/n/10.95 Thus $\OT1/ptmcm/m/n/10.95 1 + \OML/ptmcm/m/it/10.95 w[] \OT
1/ptmcm/m/n/10.95 = (\OML/ptmcm/m/it/10.95 y[]\OT1/ptmcm/m/n/10.95 )[] [] (\OML
/ptmcm/m/it/10.95 y[]\OT1/ptmcm/m/n/10.95 )[](1 + \OML/ptmcm/m/it/10.95 w[]\OT1
/ptmcm/m/n/10.95 )$ \OT1/ptm/m/n/10.95 for some $\OML/ptmcm/m/it/10.95 w[] \OMS
/pzccm/m/n/10.95 2 \OML/ptmcm/m/it/10.95 A[]$\OT1/ptm/m/n/10.95 , and so $\OT1/
ptmcm/m/n/10.95 1 + \OML/ptmcm/m/it/10.95 w \OT1/ptmcm/m/n/10.95 =
 []


LaTeX Warning: Command \textless invalid in math mode on input line 604.


LaTeX Warning: Command \textless invalid in math mode on input line 604.

[16] [17]
Chapter 4.

Underfull \hbox (badness 10000) in paragraph at lines 632--635

 []


Underfull \hbox (badness 10000) in paragraph at lines 653--656

 []


Underfull \hbox (badness 10000) in paragraph at lines 674--677

 []

[18

] [19] [20]
Underfull \hbox (badness 10000) in paragraph at lines 853--856

 []

[21]
Underfull \hbox (badness 10000) in paragraph at lines 961--964

 []

[22]
Underfull \hbox (badness 10000) in paragraph at lines 981--984

 []


Underfull \hbox (badness 10000) in paragraph at lines 1005--1011

 []

[23] [24]
Underfull \hbox (badness 1033) in paragraph at lines 1118--1120
[]\OT1/ptm/m/n/10.95 Please note that for cal-cu-la-tion of the aug-men-ta-tion
 of an el-e-ment of a group ring the
 []


Underfull \hbox (badness 1286) in paragraph at lines 1118--1120
\OT1/ptm/m/n/10.95 user is strongly rec-om-mended to use \OT1/pcr/m/n/10.95 Aug
mentation \OT1/ptm/m/n/10.95 ([][]4.2.5[][]) which works much faster than
 []

LaTeX Font Info:    Font shape `OMS/ptm/m/n' in size <10.95> not available
(Font)              Font shape `OMS/pzccm/m/n' tried instead on input line 1157
.
[25] [26]
Underfull \hbox (badness 10000) in paragraph at lines 1265--1268

 []


Underfull \hbox (badness 10000) in paragraph at lines 1286--1289

 []

[27] [28]
Underfull \hbox (badness 10000) in paragraph at lines 1403--1405
[]\OT1/ptm/m/n/10.95 The ar-gu-ment [] is a $\OML/ptmcm/m/it/10.95 p$\OT1/ptm/m
/n/10.95 -modular group al-ge-bra over the field of $\OML/ptmcm/m/it/10.95 p$ \
OT1/ptm/m/n/10.95 el-e-ments.
 []

[29] [30] [31]
Underfull \hbox (badness 10000) in paragraph at lines 1585--1588

 []


Underfull \hbox (badness 10000) in paragraph at lines 1605--1608

 []


Underfull \hbox (badness 10000) in paragraph at lines 1625--1628

 []

[32]
Underfull \hbox (badness 2762) in paragraph at lines 1653--1654
[]\OT1/ptm/m/n/10.95 If [] is the (nor-mal-ized) unit group of a $\OML/ptmcm/m/
it/10.95 p$\OT1/ptm/m/n/10.95 -modular group al-ge-bra $\OML/ptmcm/m/it/10.95 K
G$ \OT1/ptm/m/n/10.95 ob-tained us-
 []


Underfull \hbox (badness 10000) in paragraph at lines 1653--1654
\OT1/ptm/m/n/10.95 ing one of the func-tions \OT1/pcr/m/n/10.95 Units(KG)\OT1/p
tm/m/n/10.95 , \OT1/pcr/m/n/10.95 PcUnits(KG)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/
10.95 NormalizedUnitGroup(KG) \OT1/ptm/m/n/10.95 or
 []

[33] [34]
Underfull \hbox (badness 10000) in paragraph at lines 1787--1790

 []


Underfull \hbox (badness 10000) in paragraph at lines 1809--1812

 []

[35]
Underfull \hbox (badness 10000) in paragraph at lines 1897--1900

 []

[36]
Underfull \hbox (badness 10000) in paragraph at lines 1924--1927

 []

[37] [38]
Underfull \hbox (badness 10000) in paragraph at lines 2085--2088

 []

[39]
Underfull \hbox (badness 10000) in paragraph at lines 2112--2115

 []


Underfull \hbox (badness 10000) in paragraph at lines 2139--2142

 []


Underfull \hbox (badness 10000) in paragraph at lines 2166--2169

 []

[40]
Underfull \hbox (badness 10000) in paragraph at lines 2191--2194

 []

[41]
Underfull \hbox (badness 10000) in paragraph at lines 2249--2252

 []


Underfull \hbox (badness 10000) in paragraph at lines 2277--2280

 []


Underfull \hbox (badness 10000) in paragraph at lines 2304--2307

 []

[42]
Underfull \hbox (badness 10000) in paragraph at lines 2324--2327

 []


Underfull \hbox (badness 10000) in paragraph at lines 2350--2353

 []

[43]
Underfull \hbox (badness 10000) in paragraph at lines 2380--2383

 []


Underfull \hbox (badness 10000) in paragraph at lines 2402--2405

 []

[44] [45]
Underfull \hbox (badness 10000) in paragraph at lines 2505--2508

 []


Underfull \hbox (badness 10000) in paragraph at lines 2535--2538

 []


Underfull \hbox (badness 10000) in paragraph at lines 2550--2553

 []

(./manual.bbl (./manual.brf)
\tf@brf=\write9
\openout9 = `manual.brf'.

 [46]) (./manual.ind [47

]
Overfull \hbox (60.04977pt too wide) in paragraph at lines 9--11
[]\OT1/pcr/m/n/10.95 AugmentationIdealOfDerivedSubgroupNilpotencyIndex\OT1/ptm/
m/n/10.95 ,
 []


Underfull \hbox (badness 10000) in paragraph at lines 92--93
[]\OT1/pcr/m/n/10.95 NaturalBijectionToAssociativeAlgebra\OT1/ptm/m/n/10.95 ,
 []


Underfull \hbox (badness 10000) in paragraph at lines 94--96
[]\OT1/pcr/m/n/10.95 NaturalBijectionToNormalizedUnitGroup\OT1/ptm/m/n/10.95 ,
 []


Overfull \hbox (4.20505pt too wide) in paragraph at lines 96--98
[]\OT1/pcr/m/n/10.95 NaturalBijectionToPcNormalizedUnitGroup\OT1/ptm/m/n/10.95 
,
 []

[48

] [49

]) (./manual.aux)

LaTeX Warning: There were multiply-defined labels.

 ) 
Here is how much of TeX's memory you used:
 3921 strings out of 95137
 54222 string characters out of 1183013
 2098950 words of memory out of 4553785
 6813 multiletter control sequences out of 10000+50000
 66369 words of font info for 129 fonts, out of 2000000 for 2000
 58 hyphenation exceptions out of 5000
 27i,7n,30p,732b,452s stack positions out of 5000i,500n,6000p,200000b,40000s
PDF statistics:
 626 PDF objects out of 300000
 156 named destinations out of 131072
 17 words of extra memory for PDF output out of 10000
</usr/local/teTeX/share/texmf.tetex/fonts/type1/bluesky/symbols/msam10.pfb></
usr/local/teTeX/share/texmf.tetex/fonts/type1/bluesky/cm/cmex10.pfb></usr/local
/teTeX/share/texmf.tetex/fonts/type1/bluesky/cm/cmmi10.pfb></usr/local/teTeX/sh
are/texmf.tetex/fonts/type1/urw/symbol/usyr.pfb></usr/local/teTeX/share/texmf.t
etex/fonts/type1/bluesky/cm/cmr10.pfb></usr/local/teTeX/share/texmf.tetex/fonts
/type1/bluesky/cm/cmsy10.pfb>{/usr/local/teTeX/share/texmf.tetex/fonts/enc/dvip
s/psnfss/8r.enc}</usr/local/teTeX/share/texmf.tetex/fonts/type1/urw/times/utmri
8a.pfb></usr/local/teTeX/share/texmf.tetex/fonts/type1/urw/helvetic/uhvr8a.pfb>
</usr/local/teTeX/share/texmf.tetex/fonts/type1/urw/helvetic/uhvro8a.pfb></usr/
local/teTeX/share/texmf.tetex/fonts/type1/urw/courier/ucrr8a.pfb></usr/local/te
TeX/share/texmf.tetex/fonts/type1/urw/times/utmr8a.pfb></usr/local/teTeX/share/
texmf.tetex/fonts/type1/urw/times/utmb8a.pfb></usr/local/teTeX/share/texmf.tete
x/fonts/type1/urw/helvetic/uhvb8a.pfb>
Output written on manual.pdf (49 pages, 315213 bytes).
