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Ensure IsomorphismPermGroup(G) always returns an isomorphism for G (before if G was a finite matrix group it sometimes returned an isomorphism for a general linear group containing G) #5339

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Feb 1, 2023
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Ensure IsomorphismPermGroup(G) always returns an isomorphism for G (before if G was a finite matrix group it sometimes returned an isomorphism for a general linear group containing G) #5339

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622ef2a
Ensure IsomorphismPermGroup returns an isomorphism
fingolfin Jan 24, 2023
7a36c35
Adjust IsomorphismPermGroup for IsGreensHClass
fingolfin Jan 28, 2023
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7 changes: 3 additions & 4 deletions lib/grpmat.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -556,19 +556,18 @@ function(G)
local map;
if HasNiceMonomorphism(G) and IsPermGroup(Range(NiceMonomorphism(G))) then
map:=NiceMonomorphism(G);
if IsIdenticalObj(Source(map),G) then
return map;
fi;
return GeneralRestrictedMapping(map,G,NiceObject(G));
else
if not HasIsFinite(G) then
Info(InfoWarning,1,
"IsomorphismPermGroup: The group is not known to be finite");
fi;
map:=NicomorphismOfGeneralMatrixGroup(G,false,false);
SetNiceMonomorphism(G,map);
fi;
if IsIdenticalObj(Source(map),G) then
return map;
fi;
return GeneralRestrictedMapping(map,G,NiceObject(G));
end);

InstallMethod( IsomorphismPermGroup,
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7 changes: 4 additions & 3 deletions lib/semitran.gi
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Expand Up @@ -119,12 +119,12 @@ InstallMethod(IsomorphismPermGroup,
function( h )
local enum, permgroup, i, perm, j, elts;

if not(IsFinite(h)) then
if not IsFinite(h) then
# What is an example where this can happen?
TryNextMethod();
fi;

if not( IsGroupHClass(h) ) then
if not IsGroupHClass(h) then
# What is an example where this can happen?
ErrorNoReturn("can only create isomorphisms of group H-classes");
fi;
Expand All @@ -145,7 +145,8 @@ function( h )
i := i+1;
od;

return MappingByFunction( h, permgroup, a -> elts[Position( enum, a )]);
return MappingByFunction( h, permgroup, a -> elts[Position( enum, a )],
a -> enum[Position( elts, a )]);
end);

# TODO can this be removed? It doesn't seem to work
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5 changes: 5 additions & 0 deletions tst/testbugfix/2023-01-24-IsomorphismPermGroup.tst
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@@ -0,0 +1,5 @@
# see <https://github.com/gap-system/gap/issues/3601>
gap> G:=SL(2,3);;Order(G);
24
gap> P:=Image(IsomorphismPermGroup(G));;Order(P);
24
7 changes: 4 additions & 3 deletions tst/testinstall/semitran.tst
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@@ -1,5 +1,5 @@
#@local BruteForceAntiIsoCheck,BruteForceInverseCheck,BruteForceIsoCheck
#@local G,H,I,S,T,enum,inv,map
#@local G,H,I,S,T,enum,inv,map,x,y
gap> START_TEST("semitran.tst");

# Test that the inverse of an isomorphism from a partial perm monoid to a
Expand Down Expand Up @@ -145,10 +145,11 @@ gap> S := Semigroup(IdentityTransformation);
# Test IsomorphismPermGroup for an H-class
gap> S := FullTransformationMonoid(4);;
gap> H := GreensHClassOfElement(S, One(S));;
gap> IsomorphismPermGroup(H);;
gap> H := GreensHClassOfElement(S, Transformation([1, 1, 2, 3]));;
gap> map := IsomorphismPermGroup(H);;
gap> for x in H do y:=Image(map, x); Assert(0, PreImagesRepresentative(map, y) = x); od;

# The Semigroups package produces different output so this test is suppressed
#gap> H := GreensHClassOfElement(S, Transformation([1, 1, 2, 3]));;
#gap> IsomorphismPermGroup(H);
#Error, can only create isomorphisms of group H-classes

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