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# 8 Development History

### Sections

1. Versions 2.002 -- 2.005
2. Version 2.006
3. What needs doing next?

This chapter, which is intended to contain details of the major changes to the package as it develops, was first created in April 2002. Details of the changes from XMod 1 to XMod 2.001 are far from complete.

Version 1

The inspiration for this package was the need, in the mid-1990's, to calculate induced crossed modules (see citeBW1,BW2,BW3). GAP was chosen over other computational group theory systems because the code was freely available, and it was possible to modify the Tietze transformation code so as to record the images of the original generators of a presentation as words in the simplified presentation. (These modifications are now a standard part of the Tietze transformation package in GAP.)

The first version of XMod became an accepted share package for GAP 3.4.3 in December 1996.

Version 2

Conversion of XMod 1 from GAP 3.4.3 to the new GAP syntax began soon after GAP 4 was released, and had a lengthy gestation. The new GAP syntax encouraged a re-naming of many of the function names. An early decision was to introduce generic names `2dObject` for (pre-)crossed modules and (pre-)cat1-groups, and `2dMapping` for the various types of morphism. This allows `3dObject` to be used in future for crossed squares and cat2-groups, and `3dMapping` for their morphisms. A generic name for derivations and sections is also required, and `Up2dMapping` is currently used.

Version 2.001

This was the first version of XMod for GAP 4, completed in April 2002 in a rush to catch the release of GAP 4.3. Functions for actors and induced crossed modules were not included, nor many of the functions for derivations and sections, for example `InnerDerivation`. During the ten days prior to the release, the main changes made were:

·
  Generic name `UpMapping` chosen for derivations and sections (now changed to `Up2dMapping`).
·
  File names changed to `obj2.gd`, `map2.gi`, `up2.tex`, etc.
·
  Added alternative methods for `IsomorphismPermGroup` for `2dObjects`. (Strange terminology here! Will probably define global functions `IsomorphismPermObject`, `IsomorphismFpObject`, etc. in a later version which will call `IsomorphismPermGroup`, `IsomorphismPerm2dObject` or whatever is appropriate.)
·
  Sorted a problem with fixing the generating set for R when used to define derivations. The (old) code uses an fp-group version of R and checks that all the relators map by chi to 1. Unfortunately, `IsomorphismFpGroup` sometimes permutes the order of the R-generators, with unfortunate effects. The fix is to use `IsomorphismFpGroupByGenerators` which returns the images of the generators specified in the function call. We have also used `genR := StrongGeneratorsStabChain( StabChain( rng ) );` throughout to specify the generators of R.
·
  Operation `XModMorphism` renamed as `XModMorphismByHoms`, and a new global function `XModMorphism` introduced (and ditto for other `2dMappings`).
·
  Now using c1 *c2 for Whitehead multiplication

  on the right, with `CompositeDerivation` still giving multiplication

  on the left. This means that the second axiom for derivations and for sections has changed -- see Chapter 4.

## 8.1 Versions 2.002 -- 2.005

Version 2.002 was prepared for the 4.4 release at the end of January 2004, and so required a

PackageInfo.g file.

Version 2.003 of February 28th 2004 just fixed some file protections.

Version 2.004 of April 14th 2004 gave a new email address for Murat Alp and added the `Cat1Select` functionality of version 1 to the `Cat1` function (the loading mechanism was revised in version 2.006).

Version 2.005 of April 16th 2004 moved the example files from tst/test_i.g to examples/example_i.g, and converted testmanual.g to a proper test file tst/xmod_manual.tst.

Changes made include the following.

·
  Replaced `OperationHomomorphism` by `ActionHomomorphism` -- a general GAP 4.4 change.
·
  Finished replacing `RModule` by `AbelianModule`.
·
  Renamed `UpMapping` as `Up2dMapping`.
·
  Added `MappingGeneratorsImages` and `InverseGeneralMapping` for a `2dMapping`.
·
  Converted the actor crossed module functions from the 3.4.4 version, including `AutomorphismPermGroup` for a crossed module, `WhiteheadXMod`, `NorrieXMod`, `LueXMod`, `ActorXMod`, `Centre` of a crossed module, `InnerMorphism` and `InnerActorXMod`.
·
  Added `SmallerDegreePermPreXMod` after discovering `SmallerDegreePermutationRepresentation` in the library.

## 8.2 Version 2.006

This version contains changes made between May 4th and September 6th 2004.

·
  Changed morphism functions to return `fail` when invalid data is supplied, rather than calling `Error`.
·
  Fixed a bug in `XmodByGroupOfAutomorphisms`.

## 8.3 What needs doing next?

·
  Speed up the calculation of Whitehead groups.
·
  Complete the conversion from Version 1 of the calculation of sections using `EndoClasses`.
·
  Add basic functions for `3dObjects`: the actor of a crossed module is a typical example of a crossed square.
·
  Add interaction with IdRel, XRes, ntp.
·
  Need `InverseGeneralMapping` for morphisms.
·
  Need more features for `FpXMods`, `PcXMods`, etc.
·
  Implement actions of a crossed module.
·
  Implement `FreeXMods`.
·
  Implement an operation `Isomorphism2dObjects`.

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