# The GAP 4 Reference Manual - Index P

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p-adic Numbers 66.0
p-group 37.15
package 74.0
Package Interface - Obsolete Functions and Name Changes 75.2
Packages 73.6
PadicCoefficients 25.4.3
PadicExtensionNumberFamily 66.2.1
PadicNumber 66.2.2
PadicNumber, for pure padics 66.1.2
Pager 2.4.1
Parametrized 71.3.5
Parametrized Maps 71.3
parametrized maps 71.0
Parent 30.7.1
ParentPcgs 43.7.3
Parents 30.7
partial order 32.2
PartialOrderByOrderingFunction 32.4.6
PartialOrderOfHasseDiagram 32.2.11
Partitions 17.2.15
partitions, improper, of an integer 17.2
partitions, ordered, of an integer 17.2
partitions, restricted, of an integer 17.2
PartitionsGreatestEQ 17.2.20
PartitionsGreatestLE 17.2.19
PartitionsSet 17.2.13
PartitionTuples 17.2.26
Pc Groups 44.0
Pc groups versus fp groups 44.3
PcElementByExponents 43.5.6
PcElementByExponentsNC 43.5.6
PCentralLieAlgebra 61.8.5
PCentralNormalSeriesByPcgsPGroup 43.11.12
PCentralSeries 37.17.13
PcGroupCode 44.9.3
PcGroupCodeRec 44.9.4
PcGroupFpGroup 44.4.1
PcGroupWithPcgs 44.5.1
Pcgs 43.2.1
Pcgs and Normal Series 43.11
Pcgs_OrbitStabilizer 43.15.2
PcgsByPcSequence 43.3.1
PcgsByPcSequenceNC 43.3.1
PcgsCentralSeries 43.11.6
PcgsChiefSeries 43.11.14
PcgsElementaryAbelianSeries 43.11.2
PcgsPCentralSeriesPGroup 43.11.10
PClassPGroup 37.15.16
PCore 37.11.3
PcSeries 43.4.4
perfect groups 48.8
PerfectGroup 48.8.2
PerfectIdentification 48.8.3
PerfectResiduum 37.12.8
Perform 21.20.10
Permanent 17.4.1
Permanent of a Matrix 17.4
PermBounds 70.14.3
PermCharInfo 70.13.1
PermCharInfoRelative 70.13.2
PermChars 70.14.1
PermCharsTom 68.12.2
PermComb 70.14.4
PermLeftQuoTransformation 52.0
PermList 40.4.2
PermListList 21.20.11
Permutation 39.8.1
permutation character 71.5
permutation characters, possible 70.13 70.14
Permutation Groups 41.0
PermutationCharacter 70.7.3
PermutationCycle 39.8.2
PermutationMat 24.4.5
Permutations 40.0
Permutations Induced by Elements and Cycles 39.8
PermutationsFamily 40.0
PermutationsList 17.2.9
PermutationTom 68.5.2
Permuted 21.20.16
Permuted, as a permutation action 39.2.14
Permuted, for class functions 70.4
PGL 48.2.8
PGU 48.2.10
Phi 15.1.2
point stabilizer 39.4
Polycyclic Generating Systems 43.1
Polycyclic Groups 43.0
Polynomial Factorization 64.10
Polynomial Rings 64.14
PolynomialByExtRep 64.21.2
PolynomialCoefficientsOfPolynomial 64.6.2
PolynomialDivisionAlgorithm 64.16.13
PolynomialModP 64.11.2
PolynomialReducedRemainder 64.16.12
PolynomialReduction 64.16.11
PolynomialRing 64.14.1
Polynomials and Rational Functions 64.0
Polynomials as Univariate Polynomials in one Indeterminate 64.6
polynomials over abelian number fields, Factors 58.2
Polynomials over the Rationals 64.11
PopOptions 8.0
Portability 9.1
Porting GAP 73.13
Position 21.16.1
PositionBound 21.16.7
PositionCanonical 21.16.2
PositionNonZero 21.16.9
PositionNot 21.16.8
PositionNthOccurrence 21.16.3
PositionProperty 21.16.6
PositionSet 21.16.5
PositionSorted 21.16.4
PositionStream 10.3.8
PositionSublist 21.16.10
PositionWord 35.4.4
positive number 4.12.1
PositiveIntegers 14.0
PositiveRoots 61.7.7
PositiveRootVectors 61.7.9
Possible Permutation Characters 70.13
possible permutation characters 70.13 70.14
PossibleClassFusions 71.2.6
PossibleFusionsCharTableTom 68.12.1
PossiblePowerMaps 71.1.2
power 4.12.1
Power Maps 71.1
power, matrix 24.2.10
power, meaning for class functions 70.4
power, of words 35.4
PowerMap 71.1.1
PowerMapByComposition 71.1.4
PowerMapOp 71.1.1
PowerMapsAllowedBySymmetrizations 71.4.6
PowerMod 54.7.8
PowerModCoeffs 23.6.5
PowerModInt 14.2.10
PowerPartition 17.2.25
powerset 17.2
PowerSubalgebraSeries 60.8.4
PQuotient 45.13.1
precedence 4.12
precedence test, for permutations 40.1.1
PrefrattiniSubgroup 37.12.7
PrefrattiniSubgroup, for groups with pcgs 43.16
PreImage 31.4.6
PreImageElm 31.4.3
PreImages 31.4.7
Preimages in the Free Group 45.3
Preimages in the Free Semigroup 51.3
Preimages under Homomorphisms from an FpGroup 45.12
Preimages under Mappings 31.4
PreImagesElm 31.4.2
PreimagesOfTransformation 52.0
PreImagesRange 31.4.1
PreImagesRepresentative 31.4.4
PreImagesSet 31.4.5
preorder 32.2
PresentationFpGroup 46.1.1
PresentationNormalClosure 46.3.6
PresentationNormalClosureRrs 46.3.5
Presentations and Tietze Transformations 46.0
PresentationSubgroup 46.3.1
PresentationSubgroupMtc 46.3.4
PresentationSubgroupRrs 46.3.2
PresentationViaCosetTable 46.1.5
previous result 6.1
PrevPrimeInt 14.3.5
primary subgroup generators 46.11
PrimaryGeneratorWords 46.3.3
Prime Integers and Factorization 14.3
prime residue group 15.0 15.1
prime residue group, exponent 15.1
prime residue group, generator 15.2
prime residue group, order 15.1
Prime Residues 15.1
PrimeBlocks 69.9.1
PrimeBlocksOp 69.9.1
PrimeField 56.2.4
PrimePGroup 37.15.15
PrimePowersInt 14.3.8
PrimeResidues, function 15.1.1
Primes 14.3.1
primitive 39.9
Primitive Groups 41.4
Primitive Permutation Groups 48.9
primitive root modulo an integer 15.2
Primitive Roots and Discrete Logarithms 15.2
PRIMITIVE_INDICES_MAGMA 48.10.3
PrimitiveElement 56.2.3
PrimitiveGroup 48.9.1
PrimitiveGroupsIterator 48.9.3
PrimitiveIdentification 48.10.1
PrimitiveIndexIrreducibleSolvableGroup 48.11.5
PrimitivePolynomial 64.11.1
PrimitiveRoot 57.3.2
PrimitiveRootMod 15.2.3
Primitivity of Characters 72.2
Print 6.2.2
PrintAmbiguity 71.3.14
PrintArray 24.4.10
PrintCharacterTable 69.11.2
PrintFactorsInt 14.3.7
PrintFormattingStatus 10.4.9
Printing Character Tables 69.11
Printing Class Functions 70.5
Printing Presentations 46.5
Printing Tables of Marks 68.4
PrintObj 6.2.3
PrintObj, for character tables 69.11 70.5
PrintObj, for tables of marks 68.4
PrintTo 9.7.3
PrintTo, for streams 10.4.4
ProbabilityShapes 64.11.4
problems 73.9
Problems on Particular Systems 73.11
procedure call 4.15.1
procedure call with arguments 4.15.1
Procedure Calls 4.15
Process 11.1 11.1.1
Processes 11.0
PROD_GF2MAT_GF2MAT_ADVANCED 24.14.2
PROD_GF2MAT_GF2MAT_SIMPLE 24.14.1
Product 21.20.23
product, of words 35.4
product, rational functions 64.2.1
ProductCoeffs 23.6.2
ProductSpace 60.8.3
ProductX 21.21.4
ProfileFunctions 7.7.5
ProfileGlobalFunctions 7.7.7
ProfileMethods 7.7.3
ProfileOperations 7.7.1
ProfileOperationsAndMethods 7.7.2
PROFILETHRESHOLD 7.7.9
Profiling 7.7
ProjectedInducedPcgs 43.10.2
ProjectedPcElement 43.10.1
Projection 31.1.11
Projection, example for direct products 47.1
Projection, example for semidirect products 47.2
Projection, example for subdirect products 47.3
Projection, example for wreath products 47.4
Projection, for group products 47.5.2
ProjectionMap 71.3.3
projections, find all 38.9
ProjectiveActionHomomorphismMatrixGroup 42.2.2
ProjectiveActionOnFullSpace 42.2.1
ProjectiveGeneralLinearGroup 48.2.8
ProjectiveGeneralUnitaryGroup 48.2.10
ProjectiveOrder 24.13.3
ProjectiveSpecialLinearGroup 48.2.9
ProjectiveSpecialUnitaryGroup 48.2.11
ProjectiveSymplecticGroup 48.2.12
prompt 6.1
prompt, partial 6.1
Properties 13.7
Properties and Attributes for Lists 21.17
Properties and Attributes of (General) Mappings 31.2
Properties and Attributes of Binary Relations 32.2
Properties and Attributes of Matrices 24.3
Properties and Attributes of Rational Functions 64.4
Properties and basic functionality 29.2
Properties of a Lie Algebra 61.5
Properties of rewriting systems 36.3
Properties of Rings 54.4
Properties of Tables of Marks 68.8
PRump 37.12.12
PseudoRandom 28.6.3
PSL 48.2.9
PSP 48.2.12
PSp 48.2.12
PSU 48.2.11
PthPowerImage 61.8.3
PthPowerImages 61.8.2
Pure p-adic Numbers 66.1
PurePadicNumberFamily 66.1.1
PushOptions 8.0

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GAP 4 manual
May 2005