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ConstructBrace := function(hol, subgroup)
local ab, p, f, g, a, b;
ab := Image(Embedding(hol, 2));
p := [];
f := IsomorphismPermGroup(ab);
g := IsomorphismPermGroup(subgroup);
for a in ab do
if Number(subgroup, x->x*a in Image(Embedding(hol, 1))) <> 1 then
return fail;
else
Add(p, [Image(f,a), Image(g, First(subgroup, x->x*a in Image(Embedding(hol, 1))))]);
fi;
od;
return p;
end;
Brace := function(p)
local ab, gr;
ab := Group(List(p, x->x[1]));
gr := Group(List(p, x->x[2]));
return rec(
size := Size(ab),
ab := ab,
gr := gr,
p := MappingByFunction(ab, gr, x->First(p, y->IsOne(y[1]*Inverse(x)))[2]),
);
end;
BracesWithAdditiveGroup:= function(ab)
local aut, hol, c, s , p, l, f, used, m, max;
aut := AutomorphismGroup(ab);
hol := SemidirectProduct(aut, ab);
l := [];
used := [];
for c in ConjugacyClassesSubgroups(hol) do
if Size(Representative(c)) <> Size(ab) then
continue;
fi;
p := ConstructBrace(hol, Representative(c));
if not p = fail then
Add(l, p);
fi;
od;
return l;
end;
BracesWithAbelianGroupMAXIMAL:= function(ab)
local aut, hol, c, s, p, l, f, used, m, max;
aut := AutomorphismGroup(ab);
hol := SemidirectProduct(aut, ab);
l := [];
used := [];
max := ConjugacyClassesMaximalSubgroups(hol);
Print("There are ", Size(max), " conjugacy classes of maximal subgroups\n");
for m in max do
Print("Checking maximal: ", Position(max, m), " of size ", Size(Representative(m)));
if Size(Representative(m)) mod Size(ab) <> 0 or IsSolvable(Representative(m)) = false then
Print(" - Skipped!\n");
continue;
else
Print("\n");
fi;
f := Filtered(ConjugacyClassesSubgroups(Representative(m)), x->Size(Representative(x)) = Size(ab));
for c in f do
for s in c do
if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
continue;
fi;
Add(used, s);
p := ConstructBrace(hol, s);
if not p = fail then
Add(l, p);
fi;
od;
od;
od;
Print("--\n");
return l;
end;
BracesWithAbelianGroup2 := function(ab)
local gr, aut, hol, c, s, p, l, f, used;
aut := AutomorphismGroup(ab);
hol := SemidirectProduct(aut, ab);
l := [];
used := [];
for gr in AllSmallGroups(Size, Size(ab), IsSolvable, true) do
f := List(IsomorphicSubgroups(hol, gr), x->Image(x));
for s in f do
if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
continue;
fi;
Add(used, s);
p := ConstructBrace(hol, s);
if not p = fail then
Add(l, p);
fi;
od;
od;
return l;
end;
MakeList := function(n, l)
local k, x;
Print("## size ", n, "\n");
Print("BRACES[", n, "] := rec( total := -1, implemented := ", -1, ", size := ", n, ", brace := [] );\n");
for k in [1..Size(l)] do
Print("BRACES[", n, "].brace[", k, "] := rec ( size := ", n, ", perms :=\n", l[k] );
Print("\n);\n\n");
od;
return Size(l);
end;
AllSkewbraces := function(size)
local t, x, l, k, ad;
k := 1;
t := 0;
for ad in AllSmallGroups(Size, size) do
Print("id: ", IdGroup(ad), "\n");
l := BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ad)));
for x in l do
LogTo();
LogTo(Concatenation("SBsize", String(size), "_", String(k), ".dat"));
MakeList(size, l);
LogTo();
Print("found ", Size(l), "\n");
t := t+1;
od;
k := k+1;
od;
return t;
end;
AllSkewbracesByGroupId := function( id )
local t, x, l, ad, size, nr;
size := id[1];
nr := id[2];
t := 0;
ad :=SmallGroup( id );
Print("id: ", IdGroup(ad), "\n");
l := BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ad)));
for x in l do
LogTo();
LogTo(Concatenation("SBsize", String(size), "_", String(nr), ".dat"));
MakeList(size, l);
LogTo();
Print("found ", Size(l), "\n");
t := t+1;
od;
return t;
end;
AllBraces := function(size)
local x, l, ab;
l := [];
for ab in AllSmallGroups(Size, size, IsAbelian, true) do
Print("id: ", IdGroup(ab), "\n");
for x in BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ab))) do
Add(l, x);
od;
od;
return l;
end;
#IsYB := function(group)
# local f, s, ab, hol, aut, used;
#
# if not IsSolvable(group) then
# return false;
# fi;
#
# for ab in AllSmallGroups(Size, Size(group), IsAbelian, true) do
#
# aut := AutomorphismGroup(ab);
# hol := SemidirectProduct(aut, ab);
#
# used := [];
#
# f := IsomorphicSubgroups(hol, group);
#
# if f <> [] then
# for s in List(f, x->Image(x)) do
#
# if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
# continue;
# fi;
#
# Add(used, s);
#
# if ForAll(Image(Embedding(hol, 2)), a->Number(s, x->x*a in Image(Embedding(hol, 1)))=1) then
# return true;
# fi;
# od;
# fi;
# od;
# return false;
#end;
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