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# This module is part of a GAP package MAPCLASS.
# It deals with maintaining a list of small subgroups
# and generating random tuples in them.
#
# A. James, K. Magaard, S. Shpectorov 2011
#
# CheckInSubgroup(s)
# Putting a new subgroup on the list
#
InstallGlobalFunction(CheckInSubgroup,function(s,SubgroupRecord,
PrincipalFiniteGroup, PrincipalTuple, OurR)
local r,l,i;
r:=List(ConjugacyClasses(s),x->Representative(x));
l:=[];
for i in [1..OurR] do
Append(l,[Filtered(r,x->
IsConjugate(PrincipalFiniteGroup, x,
PrincipalTuple[i]))]);
od;
Append(SubgroupRecord.SmallSubgroups, [rec( subgroup:=s, classes:=l,
weight:=SubgroupRecord.InitialWeight)]);
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight +
SubgroupRecord.InitialWeight;
end);
#
# IdentifySubgroup
# Check whether or not a subgroup is on the list
#
#
InstallGlobalFunction(IdentifySubgroup,
function(s,SubgroupRecord,PrincipalFiniteGroup, PrincipalTuple, OurR)
local r;
# if the group is our full group then increase its weight
if Size(s)>SubgroupRecord.SizeCutoff then
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight-
SubgroupRecord.SmallSubgroups[1].weight;
SubgroupRecord.SmallSubgroups[1].weight:=
MinimumList([SubgroupRecord.SmallSubgroups[1].weight +
SubgroupRecord.BumpUp, SubgroupRecord.MaximumWeight]);
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight +
SubgroupRecord.SmallSubgroups[1].weight; return;
fi;
for r in SubgroupRecord.SmallSubgroups{[2..Length(SubgroupRecord.SmallSubgroups)]} do
if Size(r.subgroup)=Size(s) then
if RepresentativeAction(Centralizer( PrincipalFiniteGroup,
s.1), r.subgroup,s)<>fail then
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight-r.weight;
r.weight:=MinimumList([r.weight+SubgroupRecord.BumpUp,
SubgroupRecord.MaximumWeight]);
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight+r.weight;
return;
fi;
fi;
od;
CheckInSubgroup(s,SubgroupRecord, PrincipalFiniteGroup, PrincipalTuple, OurR);
end);
#
# AdjustSubgroupWeighting
#
InstallGlobalFunction(AdjustSubgroupWeighting,function(subgroupNumber,
SubgroupRecord)
local g;
g:=subgroupNumber;
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight -
SubgroupRecord.SmallSubgroups[g].weight;
SubgroupRecord.SmallSubgroups[g].weight:=
MinimumList([SubgroupRecord.MaximumWeight,
SubgroupRecord.SmallSubgroups[g].weight+SubgroupRecord.BumpUp]);
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight +
SubgroupRecord.SmallSubgroups[g].weight;
end);
# End
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