| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/cubefree/gap/ (GAP Algebra Version 4.15.1©) Datei vom 29.7.2025 mit Größe 2 kB |
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Quelle prelim.gd Sprache: Shell |
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############################################################################# ## #W prelim.gd Cubefree Heiko Dietrich ## ## ############################################################################## ## #P IsCubeFreeInt( n ) ## ## The output is <true> if <n> is a cubefree integer and <false> otherwise. ## DeclareProperty( "IsCubeFreeInt", IsInt ); ############################################################################## ## #P IsSquareFreeInt( n ) ## ## The output is <true> if <n> is a squarefree integer and <false> otherwise. ## DeclareProperty( "IsSquareFreeInt", IsInt ); ############################################################################# ## #F ConstructAllCFSimpleGroups( n ) ## ## The input <n> has to be a positive cubefree integer. The output is a ## complete and irredundant list of isomorphism type representatives of ## simple groups of this size. In particular, there exists either none or ## exactly one simple group of the given order. ## DeclareGlobalFunction("ConstructAllCFSimpleGroups"); ############################################################################# ## #F ConstructAllCFNilpotentGroups( n ) ## ## The input <n> has to be a positive cubefree integer. The output is a ## complete and irredundant list of isomorphism type representatives of ## nilpotent groups of this size. The groups are given as pc groups. ## DeclareGlobalFunction("ConstructAllCFNilpotentGroups"); ############################################################################# ## #F CubefreeOrderInfo( n[,bool] ) ## ## This function displays some (very vague) information about the complexity ## of the construction of the groups of (cubefree) order <n>. It returns the ## number of possible pairs <(a,b)> where <a> is the order of a Frattini-free ## group <F> with socle <S> of order <b> which has to be constructed in order ## to construct all groups of order <n>: In fact, for each of these pairs ## <(a,b)> one would have to construct up to conjugacy all subgroups of order ## <a/b> of Aut<(S)>. The sum of the numbers of these subgroups for all pairs ## <(a,b)> as above is the number of groups of order <n>. Thus the output of ## <CubeFreeOrderInfo> is a trivial lower bound for the number of groups of ## order <n>. There is no additional information displayed if <bool> is set ## to false. ## DeclareGlobalFunction("CubefreeOrderInfo");
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2026-11-04