# The GAP 4 Manual - Full Index P

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

P, Property mark-up E 2.5
p-adic Numbers R 66.0
p-group R 37.14
package R 74.0
Package Completion E 4.12
Package Interface - Obsolete Functions and Name Changes R 75.2
Packages R 73.6
PadicCoefficients R 25.4.3
PadicExtensionNumberFamily R 66.2.1
PadicNumber R 66.2.2
PadicNumber, for pure padics R 66.1.2
Pager R 2.4.1
Parametrized R 71.3.5
Parametrized Maps R 71.3
parametrized maps R 71.0
Parent R 30.7.1
ParentPcgs R 43.7.3
Parents R 30.7
Parents and Subgroups T 9.12
Partial Methods P 2.4
partial order R 32.2
PartialOrderByOrderingFunction R 32.4.6
PartialOrderOfHasseDiagram R 32.2.11
Partitions R 17.2.15
partitions, improper, of an integer R 17.2
partitions, ordered, of an integer R 17.2
partitions, restricted, of an integer R 17.2
PartitionsGreatestEQ R 17.2.20
PartitionsGreatestLE R 17.2.19
PartitionsSet R 17.2.13
PartitionTuples R 17.2.26
Pc Groups R 44.0
Pc groups versus fp groups R 44.3
PcElementByExponents R 43.5.6
PcElementByExponentsNC R 43.5.6
PCentralLieAlgebra R 61.8.5
PCentralNormalSeriesByPcgsPGroup R 43.11.12
PCentralSeries R 37.16.13
PcGroupCode R 44.9.3
PcGroupCodeRec R 44.9.4
PcGroupFpGroup R 44.4.1
PcGroupWithPcgs R 44.5.1
Pcgs R 43.2.1
Pcgs and Normal Series R 43.11
Pcgs_OrbitStabilizer R 43.15.2
PcgsByPcSequence R 43.3.1
PcgsByPcSequenceNC R 43.3.1
PcgsCentralSeries R 43.11.6
PcgsChiefSeries R 43.11.14
PcgsElementaryAbelianSeries R 43.11.2
PcgsPCentralSeriesPGroup R 43.11.10
PClassPGroup R 37.14.16
PCore R 37.10.3
PcSeries R 43.4.4
perfect groups R 48.8
PerfectGroup R 48.8.2
PerfectIdentification R 48.8.3
PerfectResiduum R 37.11.8
Perform R 21.20.10
Permanent R 17.4.1
Permanent of a Matrix R 17.4
PermBounds R 70.14.3
PermCharInfo R 70.13.1
PermCharInfoRelative R 70.13.2
PermChars R 70.14.1
PermCharsTom R 68.12.2
PermComb R 70.14.4
PermGroupOps.ElementProperty T 9.3.4
PermLeftQuoTransformation R 52.0
PermList R 40.4.2
PermListList R 21.20.11
Permutation R 39.8.1
permutation character R 71.5
permutation characters, possible R 70.13 R 70.14
Permutation Groups R 41.0
Permutation groups T 5.1
PermutationCharacter R 70.7.3
PermutationCycle R 39.8.2
PermutationMat R 24.4.5
Permutations R 40.0
Permutations Induced by Elements and Cycles R 39.8
PermutationsFamily R 40.0
PermutationsList R 17.2.9
PermutationTom R 68.5.2
Permuted R 21.20.16
Permuted, as a permutation action R 39.2.14
Permuted, for class functions R 70.4
PGL R 48.2.8
PGU R 48.2.10
Phi R 15.1.2
Plain Lists T 3.1
Plain Records T 3.9
point stabilizer R 39.4
Polycyclic Generating Systems R 43.1
Polycyclic Groups R 43.0
Polynomial Factorization R 64.10
Polynomial Rings R 64.14
PolynomialByExtRep R 64.21.2
PolynomialCoefficientsOfPolynomial R 64.6.2
PolynomialDivisionAlgorithm R 64.16.13
PolynomialModP R 64.11.2
PolynomialReducedRemainder R 64.16.12
PolynomialReduction R 64.16.11
PolynomialRing R 64.14.1
Polynomials T 9.17
Polynomials and Rational Functions R 64.0
Polynomials as Univariate Polynomials in one Indeterminate R 64.6
polynomials over abelian number fields, Factors R 58.2
Polynomials over the Rationals R 64.11
PopOptions R 8.0
Portability R 9.1
Porting GAP R 73.13
Position R 21.16.1
Position T 9.3.3
Position vs. PositionCanonical T 5.2
Positional Objects P 3.10
PositionBound R 21.16.7
PositionCanonical R 21.16.2
PositionNonZero R 21.16.9
PositionNot R 21.16.8
PositionNthOccurrence R 21.16.3
PositionProperty R 21.16.6
PositionSet R 21.16.5
PositionSorted R 21.16.4
PositionStream R 10.3.8
PositionSublist R 21.16.10
PositionWord R 35.4.4
positive number R 4.12.1
PositiveIntegers R 14.0
PositiveRoots R 61.7.7
PositiveRootVectors R 61.7.9
Possible Permutation Characters R 70.13
possible permutation characters R 70.13 R 70.14
PossibleClassFusions R 71.2.6
PossibleFusionsCharTableTom R 68.12.1
PossiblePowerMaps R 71.1.2
power R 4.12.1
power, matrix R 24.2.10
power, meaning for class functions R 70.4
power, of words R 35.4
Power Maps R 71.1
PowerMap R 71.1.1
PowerMapByComposition R 71.1.4
PowerMapOp R 71.1.1
PowerMapsAllowedBySymmetrizations R 71.4.6
PowerMod R 54.7.8
PowerModCoeffs R 23.6.5
PowerModInt R 14.2.10
PowerPartition R 17.2.25
powerset R 17.2
PowerSubalgebraSeries R 60.8.4
PQuotient R 45.13.1
precedence R 4.12
precedence test, for permutations R 40.1.1
Preface T 1.0
PreferredGenerators N 4.2.10
PrefrattiniSubgroup R 37.11.7
PrefrattiniSubgroup, for groups with pcgs R 43.16
PreImage R 31.4.6
PreImageElm R 31.4.3
PreImages R 31.4.7
Preimages in the Free Group R 45.3
Preimages in the Free Semigroup R 51.3
Preimages under Homomorphisms from an FpGroup R 45.12
Preimages under Mappings R 31.4
PreImagesElm R 31.4.2
PreimagesOfTransformation R 52.0
PreImagesRange R 31.4.1
PreImagesRepresentative R 31.4.4
PreImagesSet R 31.4.5
preorder R 32.2
PresentationFpGroup R 46.1.1
PresentationNormalClosure R 46.3.6
PresentationNormalClosureRrs R 46.3.5
Presentations and Tietze Transformations R 46.0
PresentationSubgroup R 46.3.1
PresentationSubgroupMtc R 46.3.4
PresentationSubgroupRrs R 46.3.2
PresentationViaCosetTable R 46.1.5
previous result R 6.1
PrevPrimeInt R 14.3.5
primary subgroup generators R 46.11
PrimaryGeneratorWords R 46.3.3
Prime Integers and Factorization R 14.3
prime residue group, exponent R 15.1
prime residue group, generator R 15.2
prime residue group, order R 15.1
prime residue group R 15.0 R 15.1
Prime Residues R 15.1
PrimeBlocks R 69.9.1
PrimeBlocksOp R 69.9.1
PrimeField R 56.2.4
PrimePGroup R 37.14.15
PrimePowersInt R 14.3.8
PrimeResidues, function R 15.1.1
Primes R 14.3.1
primitive R 39.9
Primitive Groups R 41.4
Primitive Permutation Groups R 48.9
primitive root modulo an integer R 15.2
Primitive Roots and Discrete Logarithms R 15.2
PRIMITIVE_INDICES_MAGMA R 48.10.3
PrimitiveElement R 56.2.3
PrimitiveGroup R 48.9.1
PrimitiveGroupsIterator R 48.9.3
PrimitiveIdentification R 48.10.1
PrimitiveIndexIrreducibleSolvableGroup R 48.11.5
PrimitivePolynomial R 64.11.1
PrimitiveRoot R 57.3.2
PrimitiveRootMod R 15.2.3
Primitivity of Characters R 72.2
Print R 6.2.2
Print T 9.3.5
PrintAmbiguity R 71.3.14
PrintArray R 24.4.10
PrintCharacterTable R 69.11.2
PrintFactorsInt R 14.3.7
PrintFormattingStatus R 10.4.9
PrintHashWithNames N 2.3.2
Printing Character Tables R 69.11
Printing Class Functions R 70.5
Printing Presentations R 46.5
Printing Tables of Marks R 68.4
PrintObj R 6.2.3
PrintObj, for character tables R 69.11 R 70.5
PrintObj, for tables of marks R 68.4
PrintTo R 9.7.3
PrintTo, for streams R 10.4.4
PrintTo T 9.3.6
ProbabilityShapes R 64.11.4
problems R 73.9
Problems on Particular Systems R 73.11
procedure call R 4.15.1
procedure call with arguments R 4.15.1
Procedure Calls R 4.15
Process R 11.1 R 11.1.1
Processes R 11.0
PROD_GF2MAT_GF2MAT_ADVANCED R 24.14.2
PROD_GF2MAT_GF2MAT_SIMPLE R 24.14.1
Producing a Manual E 2.13
Product R 21.20.23
product, of words R 35.4
product, rational functions R 64.2.1
ProductCoeffs R 23.6.2
ProductSpace R 60.8.3
ProductX R 21.21.4
ProfileFunctions R 7.7.5
ProfileGlobalFunctions R 7.7.7
ProfileMethods R 7.7.3
ProfileOperations R 7.7.1
ProfileOperationsAndMethods R 7.7.2
PROFILETHRESHOLD R 7.7.9
Profiling R 7.7
ProjectedInducedPcgs R 43.10.2
ProjectedPcElement R 43.10.1
Projection R 31.1.11
Projection, example for direct products R 47.1
Projection, example for semidirect products R 47.2
Projection, example for subdirect products R 47.3
Projection, example for wreath products R 47.4
Projection, for group products R 47.5.2
Projection N 4.4.1
ProjectionMap R 71.3.3
projections, find all R 38.9
ProjectiveActionHomomorphismMatrixGroup R 42.2.2
ProjectiveActionOnFullSpace R 42.2.1
ProjectiveGeneralLinearGroup R 48.2.8
ProjectiveGeneralUnitaryGroup R 48.2.10
ProjectiveOrder R 24.13.3
ProjectiveSpecialLinearGroup R 48.2.9
ProjectiveSpecialUnitaryGroup R 48.2.11
ProjectiveSymplecticGroup R 48.2.12
prompt R 6.1
prompt, partial R 6.1
Properties R 13.7
Properties and Attributes for Lists R 21.17
Properties and Attributes of (General) Mappings R 31.2
Properties and Attributes of Binary Relations R 32.2
Properties and Attributes of Matrices R 24.3
Properties and Attributes of Rational Functions R 64.4
Properties and basic functionality R 29.2
Properties and Filters T 8.2
Properties of a Lie Algebra R 61.5
Properties of rewriting systems R 36.3
Properties of Rings R 54.4
Properties of Tables of Marks R 68.8
PRump R 37.11.12
PseudoRandom R 28.6.3
PSL R 48.2.9
PSP R 48.2.12
PSp R 48.2.12
PSU R 48.2.11
PthPowerImage R 61.8.3
PthPowerImages R 61.8.2
Pure p-adic Numbers R 66.1
PurePadicNumberFamily R 66.1.1
PushOptions R 8.0

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