\indexentry{LAGUNA package@\textsf{LAGUNA} package|hyperpage}{2} \indexentry{SISYPHOS package@\textsf{SISYPHOS} package|hyperpage}{6} \indexentry{group algebra|hyperpage}{14} \indexentry{augmentation homomorphism|hyperpage}{14} \indexentry{augmentation ideal|hyperpage}{14} \indexentry{unit|hyperpage}{14} \indexentry{unit group|hyperpage}{14} \indexentry{normalised unit|hyperpage}{14} \indexentry{normalised unit group|hyperpage}{14} \indexentry{p-modular group algebra@$p$-modular group algebra|hyperpage}{15} \indexentry{power-commutator presentation|hyperpage}{15} \indexentry{Jennings series|hyperpage}{15} \indexentry{dimension basis|hyperpage}{15} \indexentry{weight, of dimension basis element|hyperpage}{15} \indexentry{standard product|hyperpage}{15} \indexentry{IsGroupAlgebra@\texttt {IsGroupAlgebra}|hyperpage}{18} \indexentry{IsFModularGroupAlgebra@\texttt {IsFModularGroupAlgebra}|hyperpage}{18} \indexentry{modular group algebra|hyperpage}{18} \indexentry{IsPModularGroupAlgebra@\texttt {IsPModularGroupAlgebra}|hyperpage}{19} \indexentry{UnderlyingGroup@\texttt {UnderlyingGroup}!of a group ring|hyperpage}{19} \indexentry{UnderlyingRing@\texttt {UnderlyingRing}|hyperpage}{19} \indexentry{UnderlyingField@\texttt {UnderlyingField}|hyperpage}{20} \indexentry{Support@\texttt {Support}|hyperpage}{20} \indexentry{CoefficientsBySupport@\texttt {CoefficientsBySupport}|hyperpage}{20} \indexentry{TraceOfMagmaRingElement@\texttt {TraceOfMagmaRingElement}|hyperpage}{21} \indexentry{Length@\texttt {Length}|hyperpage}{21} \indexentry{Augmentation@\texttt {Augmentation}|hyperpage}{21} \indexentry{PartialAugmentations@\texttt {PartialAugmentations}|hyperpage}{22} \indexentry{partial augmentation|hyperpage}{22} \indexentry{Involution@\texttt {Involution}|hyperpage}{22} \indexentry{Involution@\texttt {Involution}|hyperpage}{22} \indexentry{IsSymmetric@\texttt {IsSymmetric}|hyperpage}{23} \indexentry{symmetric element|hyperpage}{23} \indexentry{IsUnitary@\texttt {IsUnitary}|hyperpage}{23} \indexentry{unitary element|hyperpage}{23} \indexentry{IsUnit@\texttt {IsUnit}|hyperpage}{23} \indexentry{IsUnit@\texttt {IsUnit}|hyperpage}{23} \indexentry{InverseOp@\texttt {InverseOp}|hyperpage}{24} \indexentry{BicyclicUnitOfType1@\texttt {BicyclicUnitOfType1}|hyperpage}{24} \indexentry{BicyclicUnitOfType1@\texttt {BicyclicUnitOfType1}|hyperpage}{24} \indexentry{BicyclicUnitOfType2@\texttt {BicyclicUnitOfType2}|hyperpage}{24} \indexentry{BicyclicUnitOfType2@\texttt {BicyclicUnitOfType2}|hyperpage}{24} \indexentry{bicyclic unit|hyperpage}{24} \indexentry{AugmentationHomomorphism@\texttt {AugmentationHomomorphism}|hyperpage}{25} \indexentry{AugmentationIdeal@\texttt {AugmentationIdeal}|hyperpage}{25} \indexentry{RadicalOfAlgebra@\texttt {RadicalOfAlgebra}|hyperpage}{26} \indexentry{WeightedBasis@\texttt {WeightedBasis}|hyperpage}{26} \indexentry{AugmentationIdealPowerSeries@\texttt {AugmentationIdealPowerSeries}|hyperpage}{27} \indexentry{AugmentationIdealNilpotencyIndex@\texttt {AugmentationIdealNilpotencyIndex}|hyperpage}{27} \indexentry{AugmentationIdealOfDerivedSubgroupNilpotencyIndex@\texttt {AugmentationIdealOfDerivedSubgroupNilpotencyIndex}|hyperpage}{27} \indexentry{LeftIdealBySubgroup@\texttt {LeftIdealBySubgroup}|hyperpage}{28} \indexentry{RightIdealBySubgroup@\texttt {RightIdealBySubgroup}|hyperpage}{28} \indexentry{TwoSidedIdalBySubgroup@\texttt {TwoSidedIdalBySubgroup}|hyperpage}{28} \indexentry{LeftIdealBySubgroup@\texttt {LeftIdealBySubgroup}|hyperpage}{28} \indexentry{NormalizedUnitGroup@\texttt {NormalizedUnitGroup}|hyperpage}{29} \indexentry{PcNormalizedUnitGroup@\texttt {PcNormalizedUnitGroup}|hyperpage}{29} \indexentry{NaturalBijectionToPcNormalizedUnitGroup@\texttt {NaturalBijectionToPcNormalizedUnitGroup}|hyperpage}{29} \indexentry{NaturalBijectionToNormalizedUnitGroup@\texttt {NaturalBijectionToNormalizedUnitGroup}|hyperpage}{30} \indexentry{Embedding@\texttt {Embedding}|hyperpage}{30} \indexentry{Units@\texttt {Units}|hyperpage}{31} \indexentry{PcUnits@\texttt {PcUnits}|hyperpage}{32} \indexentry{IsGroupOfUnitsOfMagmaRing@\texttt {IsGroupOfUnitsOfMagmaRing}|hyperpage}{32} \indexentry{IsUnitGroupOfGroupRing@\texttt {IsUnitGroupOfGroupRing}|hyperpage}{32} \indexentry{IsNormalizedUnitGroupOfGroupRing@\texttt {IsNormalizedUnitGroupOfGroupRing}|hyperpage}{33} \indexentry{UnderlyingGroupRing@\texttt {UnderlyingGroupRing}|hyperpage}{33} \indexentry{UnitarySubgroup@\texttt {UnitarySubgroup}|hyperpage}{33} \indexentry{BicyclicUnitGroup@\texttt {BicyclicUnitGroup}|hyperpage}{34} \indexentry{AugmentationIdealPowerFactorGroup@\texttt {AugmentationIdealPowerFactorGroup}|hyperpage}{34} \indexentry{GroupBases@\texttt {GroupBases}|hyperpage}{35} \indexentry{LieAlgebraByDomain@\texttt {LieAlgebraByDomain}|hyperpage}{35} \indexentry{IsLieAlgebraByAssociativeAlgebra@\texttt {IsLieAlgebraByAssociativeAlgebra}|hyperpage}{36} \indexentry{UnderlyingAssociativeAlgebra@\texttt {UnderlyingAssociativeAlgebra}|hyperpage}{36} \indexentry{NaturalBijectionToLieAlgebra@\texttt {NaturalBijectionToLieAlgebra}|hyperpage}{36} \indexentry{NaturalBijectionToAssociativeAlgebra@\texttt {NaturalBijectionToAssociativeAlgebra}|hyperpage}{37} \indexentry{IsLieAlgebraOfGroupRing@\texttt {IsLieAlgebraOfGroupRing}|hyperpage}{37} \indexentry{UnderlyingGroup@\texttt {UnderlyingGroup}!of Lie algebra of a group ring|hyperpage}{38} \indexentry{Embedding@\texttt {Embedding}|hyperpage}{38} \indexentry{LieCentre@\texttt {LieCentre}|hyperpage}{39} \indexentry{LieDerivedSubalgebra@\texttt {LieDerivedSubalgebra}|hyperpage}{39} \indexentry{IsLieAbelian@\texttt {IsLieAbelian}|hyperpage}{40} \indexentry{IsLieSolvable@\texttt {IsLieSolvable}|hyperpage}{40} \indexentry{IsLieNilpotent@\texttt {IsLieNilpotent}|hyperpage}{41} \indexentry{IsLieMetabelian@\texttt {IsLieMetabelian}|hyperpage}{41} \indexentry{IsLieCentreByMetabelian@\texttt {IsLieCentreByMetabelian}|hyperpage}{41} \indexentry{CanonicalBasis@\texttt {CanonicalBasis}|hyperpage}{42} \indexentry{IsBasisOfLieAlgebraOfGroupRing@\texttt {IsBasisOfLieAlgebraOfGroupRing}|hyperpage}{42} \indexentry{StructureConstantsTable@\texttt {StructureConstantsTable}|hyperpage}{43} \indexentry{LieUpperNilpotencyIndex@\texttt {LieUpperNilpotencyIndex}|hyperpage}{43} \indexentry{upper Lie power series|hyperpage}{43} \indexentry{LieLowerNilpotencyIndex@\texttt {LieLowerNilpotencyIndex}|hyperpage}{43} \indexentry{lower Lie power series|hyperpage}{43} \indexentry{LieDerivedLength@\texttt {LieDerivedLength}|hyperpage}{44} \indexentry{Lie derived series|hyperpage}{44} \indexentry{Lie derived length|hyperpage}{44} \indexentry{SubgroupsOfIndexTwo@\texttt {SubgroupsOfIndexTwo}|hyperpage}{44} \indexentry{DihedralDepth@\texttt {DihedralDepth}|hyperpage}{45} \indexentry{DimensionBasis@\texttt {DimensionBasis}|hyperpage}{45} \indexentry{LieDimensionSubgroups@\texttt {LieDimensionSubgroups}|hyperpage}{45} \indexentry{LieUpperCodimensionSeries@\texttt {LieUpperCodimensionSeries}|hyperpage}{46} \indexentry{LieUpperCodimensionSeries@\texttt {LieUpperCodimensionSeries}|hyperpage}{46} \indexentry{LAGInfo@\texttt {LAGInfo}|hyperpage}{46} \indexentry{LAGUNABuildManual@\texttt {LAGUNABuildManual}|hyperpage}{47} \indexentry{LAGUNABuildManualHTML@\texttt {LAGUNABuildManualHTML}|hyperpage}{47}