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#############################################################################
## createTables.gi
#############################################################################
##
## This file is part of the LINS package.
##
## This file's authors include Friedrich Rober.
##
## Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
#############################################################################
# Info Level 1: print every entry
DeclareInfoClass( "InfoLINS_CreateTargets" );
SetInfoLevel( InfoLINS_CreateTargets, 0 );
BindGlobal("LINS_Targets_ExponentBounds",
function(T, minIndex, maxIndex)
local minExp, maxExp;
maxExp := 1;
while Order(T) ^ (maxExp + 1) <= maxIndex do
maxExp := maxExp + 1;
od;
minExp := 1;
while Order(T) ^ (minExp) <= minIndex do
minExp := minExp + 1;
od;
if minExp > maxExp then
return fail;
fi;
return [minExp, maxExp];
end);
BindGlobal("LINS_SaveTargetsQuotients",
function(targets)
local stream, entry, M, L, tenToL, i, t;
stream := OutputTextFile("tmp", false);
SetPrintFormattingStatus(stream, false);
M := Maximum(List(targets, t -> t[1]));
# Length of Largest Number
L := 1;
tenToL := 10;
while tenToL <= M do
L := L + 1;
tenToL := tenToL * 10;
od;
for i in [1 .. Length(targets)] do
t := targets[i];
if i = 1 then
AppendTo(stream, "[ ");
else
AppendTo(stream, " ");
fi;
AppendTo(stream, "[ ", String(t[1], L), ", \"", t[2], "\", \"", t[3], "\" ]");
if i = Length(targets) then
AppendTo(stream, " ]\n");
else
AppendTo(stream, ",\n");
fi;
od;
end);
#############################################################################
## Computation of LINS_TargetsQuotient table from minIndex to maxIndex.
## Return the requested part of the table.
## Will compute information on all targets Inn(T^d) <= Q <= Aut(T^d)
## such that minIndex < |T|^d <= maxIndex.
#############################################################################
BindGlobal("LINS_CreateTargetsQuotient",
function(minIndex , maxIndex, UseLIS...)
local targets, itSimple, T, boundsExp, minExp, maxExp, d, Td, factors, aut, inn, nice, hom, G, H, K, L, perms, g, images, i, j, t, Q, subgroups, S, core, entry;
if Length(UseLIS) > 1 then
Error("Unknown number of arguments!");
elif Length(UseLIS) = 1 then
UseLIS := UseLIS[1];
else
UseLIS := false;
fi;
targets := [];
itSimple := SimpleGroupsIterator(1, maxIndex);
for T in itSimple do
# Establish exponent bounds.
boundsExp := LINS_Targets_ExponentBounds(T, minIndex, maxIndex);
if boundsExp = fail then
continue;
fi;
minExp := boundsExp[1];
maxExp := boundsExp[2];
# Iterate trough possible exponents d.
for d in [minExp .. maxExp] do
Td := DirectProduct(ListWithIdenticalEntries(d, T));
factors := List([1 .. d], i -> Image(Embedding(Td, i)));
aut := AutomorphismGroup(Td);
inn := InnerAutomorphismsAutomorphismGroup(aut);
nice := NiceMonomorphism(aut);
hom := NaturalHomomorphismByNormalSubgroup(Image(nice, aut), Image(nice, inn));
G := Image(hom);
L := LowIndexSubgroups(G, Order(G));
for H in L do
Q := PreImage(hom, H);
K := PreImage(nice, Q);
# Construct action of Q on direct factors
perms := [];
for g in GeneratorsOfGroup(K) do
images := [];
for i in [1 .. d] do
t := GeneratorsOfGroup(factors[i])[1] ^ g;
j := PositionProperty(factors, Tj -> t in Tj);
Add(images, j);
od;
Add(perms, PermList(images));
od;
# Check if action is transitive.
if IsTransitive(Group(perms), [1..d]) then
if UseLIS then
# Search for subgroup S with small index such that Core(Q, S) is trivial.
subgroups := List(MaximalSubgroupClassReps(Q));
SortBy(subgroups, s -> Index(Q, s));
while not IsEmpty(subgroups) do
S := Remove(subgroups,1);
core := Core(Q,S);
if IsTrivial(core) then
entry := [Order(Q), Index(Q, S), Concatenation(Name(T),"^",String(d))];
Info(InfoLINS_CreateTargets, 1, entry);
Add(targets, entry);
break;
else
Append(subgroups, List(MaximalSubgroupClassReps(core)));
SortBy(subgroups, s -> Index(Q, s));
fi;
od;
else
entry := [Order(Q), LINS_StringGroup(Q), Concatenation(Name(T), "^", String(d))];
Info(InfoLINS_CreateTargets, 1, entry);
Add(targets, entry);
fi;
fi;
od;
od;
od;
targets := DuplicateFreeList(targets);
Sort(targets);
return targets;
end);
#############################################################################
## Computation of LINS_TargetsCharSimple table.
## Return the requested part of the table.
## Will compute the primes dividing the schur multiplier of all groups T^d
## such that minIndex < |T|^d <= maxIndex.
## Dependent on cohomolo package.
#############################################################################
BindGlobal("LINS_CreateTargetsCharSimple",
function(minIndex, maxIndex)
local targets, itSimple, T, boundsExp, minExp, maxExp, mult, p, d, entry;
targets := [];
itSimple := SimpleGroupsIterator(1, maxIndex);
for T in itSimple do
# Establish exponent bounds.
boundsExp := LINS_Targets_ExponentBounds(T, minIndex, maxIndex);
if boundsExp = fail then
continue;
fi;
minExp := boundsExp[1];
maxExp := boundsExp[2];
# Add all primes that divide SchurMultiplier of T to mult
mult := [];
for p in PrimeDivisors(Order(T)) do
if not IsEmpty(SchurMultiplier(CHR(T, p))) then
Add(mult, p);
fi;
od;
# Construct List of SchurMultipliers for groups T^d
for d in [minExp .. maxExp] do
entry := [Order(T) ^ d, List(mult), Concatenation(Name(T), "^", String(d))];
Info(InfoLINS_CreateTargets, 1, entry);
Add(targets, entry);
od;
od;
Sort(targets);
return targets;
end);
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