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#############################################################################
##
#W prelim.gd Cubefree Heiko Dietrich
##
##
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##
#P IsCubeFreeInt( n )
##
## The output is <true> if <n> is a cubefree integer and <false> otherwise.
##
DeclareProperty( "IsCubeFreeInt", IsInt );
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##
#P IsSquareFreeInt( n )
##
## The output is <true> if <n> is a squarefree integer and <false> otherwise.
##
DeclareProperty( "IsSquareFreeInt", IsInt );
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##
#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");
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##
#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");
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##
#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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