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#############################################################################
##
## util.gd CRISP Burkhard Höfling
##
## Copyright © 2000-2002, 2005 Burkhard Höfling
##
#############################################################################
##
#F CRISP_RedispatchOnCondition
##
## use six argument version of RedispatchOnCondition if it's available,
## otherwise just pass five of the six arguments
##
DeclareGlobalFunction("CRISP_RedispatchOnCondition");
if NumberArgumentsFunction(RedispatchOnCondition) = 5 then
InstallGlobalFunction(CRISP_RedispatchOnCondition,
function(oper, info, fampred, reqs, cond, val)
RedispatchOnCondition(oper, fampred, reqs, cond, val);
end);
else
InstallGlobalFunction(CRISP_RedispatchOnCondition, RedispatchOnCondition);
fi;
#############################################################################
##
#A NormalGeneratorsOfNilpotentResidualNilpotentResidual
##
## the normal closure of the subgroup generated by these elements
## is the nilpotent residual(i.e., last term of the lower central series)
##
DeclareAttribute("NormalGeneratorsOfNilpotentResidual", IsGroup);
#############################################################################
##
#F CompositionSeriesElAbFactorUnderAction(<act>, <M>, <N>)
##
## computes a <act>-composition series of the elementary abelian normal section M/N,
## i.e. a list M = N_0 > N_1 > ... > N_r = N of subgroups of <grp> such that
## there is no <grp>-invariant subgroup between N_i and N_{i+1}.
##
DeclareGlobalFunction("CompositionSeriesElAbFactorUnderAction");
#############################################################################
##
#F PcgsCompositionSeriesElAbModuloPcgsUnderAction(<act>, <sec>)
##
## computes a series of pcgs representing a <grp>-composition series of the
## elementary abelian normal section M/N,
## i.e. a list M = N_0 > N_1 > ... > N_r = N of subgroups of <grp> such that
## there is no <grp>-invariant subgroup between N_i and N_{i+1}.
##
DeclareGlobalFunction("PcgsCompositionSeriesElAbModuloPcgsUnderAction");
#############################################################################
##
#F IsAbelianModuloPcgs(<pcgs>)
##
## tests whether pcgs(regarded as factor group) is abelian
##
DeclareGlobalFunction("IsAbelianModuloPcgs");
#############################################################################
##
#O CentralizesLayer(<list>, <mpcgs>)
##
DeclareOperation("CentralizesLayer", [IsListOrCollection, IsModuloPcgs]);
#############################################################################
##
#O CompositionSeriesUnderAction(<act>, <grp>)
##
DeclareOperation("CompositionSeriesUnderAction",
[IsListOrCollection, IsGroup]);
#############################################################################
##
#F PcgsElementaryAbelianSeriesFromPrimeOrdersPcgs(<G>)
##
## computes a pcgs exhibiting an elementary abelian series of G
## from a given pcgs, avoiding SpecialPcgs. In particular returns the family
## pcgs if it has the required property
##
DeclareGlobalFunction("PcgsElementaryAbelianSeriesFromPrimeOrdersPcgs");
#############################################################################
##
#O SiftedPcElementWrtPcSequence(<pcgs>, <seq>, <depths>, <x>)
##
## sifts an element x through a pc sequence <seq>(that is, a plain list
## whose elements form a(modulo) pcgs), reducing <x> if it has the same
## depth(wrt. the pcgs <pcgs>) as an element in seq. It returns the
## sifted element. <depths> must be a list containing for each element
## in seq its depth wrt. <pcgs>.
##
DeclareOperation("SiftedPcElementWrtPcSequence",
[IsPcgs, IsListOrCollection, IsList, IsMultiplicativeElementWithInverse]);
#############################################################################
##
#O AddPcElementToPcSequence(<pcgs>, <seq>, <depths>, <x>)
##
## sifts an element <x> through a pc sequence <seq> reducing <x> if it has
## the same depth(wrt. the pcgs <pcgs>) as an element in <seq>. If the
## resulting element is nontrivial, it is inserted at the
## appropriate position in <seq>, and the list <depths>, which must be a
## list containing for each element in <seq> its depth wrt. <pcgs>,
## is adjusted accordingly. In this case, AddPcElementToPcSequence returns
## true. Otherwise it returns false.
##
DeclareOperation("AddPcElementToPcSequence",
[IsPcgs, IsListOrCollection, IsList, IsMultiplicativeElementWithInverse]);
#############################################################################
##
#A PrimePowerGensPcSequence(<grp>)
##
## returns a record with components `primes', `generators', and `pcgs'.
## `pcgs' contains a pcgs of <grp>
## `primes' contains the set of all prime divisors of <grp>, and
## `generators' contains a list of group elements, such that the elements in
## generators[i] have relative order primes[i] and order a power of primes[i].
## In addition, the list obtained by concatenating all lists in generators
## forms a pcgs of <grp> when sorted according to their depths wrt. pcgs.
DeclareAttribute("PrimePowerGensPcSequence", IsGroup);
#############################################################################
##
#F InstallMethodByNiceMonomorphismForGroupAndClass( <oper>, <filt1>, <filt2>)
##
## install method for oper taking a group and a class
BindGlobal( "InstallMethodByNiceMonomorphismForGroupAndClass",
function( oper, filt1, filt2)
InstallMethod(oper,
"handled by nice monomorphism",
true,
[IsGroup and IsHandledByNiceMonomorphism and filt1, filt2],
0,
function( grp, class)
return PreImagesSet(NiceMonomorphism(grp),
oper(NiceObject(grp), class) );
end);
end);
#############################################################################
##
#F InstallMethodByNiceMonomorphismForGroupAndClassReturningBool(
## <oper>, <filt1>, <filt2>)
##
BindGlobal( "InstallMethodByNiceMonomorphismForGroupAndBool",
function( oper, filt1, filt2)
InstallMethod(oper,
"handled by nice monomorphism",
true,
[IsGroup and IsHandledByNiceMonomorphism and filt1, filt2],
0,
function( grp, class)
return oper(NiceObject(grp), class);
end);
end);
#############################################################################
##
#F InstallMethodByIsomorphismPcGroupForGroupAndClass( <oper>, <filt1>, <filt2>)
##
## install method for oper taking a group and a class
BindGlobal( "InstallMethodByIsomorphismPcGroupForGroupAndClass",
function( oper, filt1, filt2)
InstallMethod(oper,
"handled by IsomorphismPcGroup",
true,
[IsGroup and IsSolvableGroup and filt1, filt2],
0,
function( grp, class)
local iso;
if CanEasilyComputePcgs(grp) then
TryNextMethod();
fi;
iso := IsomorphismPcGroup(grp);
return PreImagesSet(iso,
oper(ImagesSource(iso), class) );
end);
end);
#############################################################################
##
#F InstallMethodByIsomorphismPcGroupForGroupAndClassReturningBool(
## <oper>, <filt1>, <filt2>)
##
BindGlobal( "InstallMethodByIsomorphismPcGroupForGroupAndClassReturningBool",
function( oper, filt1, filt2)
InstallMethod(oper,
"handled by IsomorphismPcGroup",
true,
[IsGroup and IsSolvableGroup and filt1, filt2],
0,
function( grp, class)
if CanEasilyComputePcgs(grp) then
TryNextMethod();
fi;
return oper(ImagesSource(IsomorphismPcGroup(grp)), class);
end);
end);
#############################################################################
##
#A CRISP_SmallGeneratingSet
##
## version of SmallGeneratingSet which does not try very hard
##
DeclareAttribute("CRISP_SmallGeneratingSet", IsGroup);
#############################################################################
##
#E
##
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