IsomorphismSemigroup to a McAlister triple semigroup can give incorrect results

[wilfwilson]

I discovered this in by running SemigroupsTestExtreme();. The bug is present in both master and stable-3.1.

gap> S := InverseMonoid([PartialPerm([2, 1])], PartialPerm([1, 2, 3]));
<inverse partial perm monoid of rank 3 with 2 generators>
gap> IsEUnitaryInverseSemigroup(S);
true
gap> iso := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, S);
MappingByFunction( <inverse partial perm monoid of size 3, rank 3 with 2
 generators>, <McAlister triple semigroup over Group([ (1,
2) ])>, function( s ) ... end )
gap> IsInjective(iso);
false
gap> T := Range(iso);
<McAlister triple semigroup over Group([ (1,2) ])>
gap> Size(T);
2

Note that the S is an example of a(n inverse) monoid of partial perms where the One of the identity acts on a larger number of points than the One of all the other elements. This is a possible root cause of the bug, especially as the resulting semigroup lacks only a single element (probably corresponding to the identity). But who knows.

[ChristopherRussell]

Thanks @wilfwilson. Things seem to work after enumerating the elements.

gap> S := InverseMonoid([PartialPerm([2, 1])], PartialPerm([1, 2, 3]));
<inverse partial perm monoid of rank 3 with 2 generators>
gap> iso := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, S);
MappingByFunction( <inverse partial perm monoid of size 3, rank 3 with 2 generators>
 , <McAlister triple semigroup over Group([ (1,2) ])>, function( s ) ... end )
gap> T := Range(iso);
<McAlister triple semigroup over Group([ (1,2) ])>
gap> Size(T);
2
gap> IsInjective(iso);
false
gap> Elements(T);
[ (1, ()), (1, (1,2)), (2, ()) ]
gap> iso := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, S);
MappingByFunction( <inverse partial perm monoid of size 3, rank 3 with 2 generators>
 , <McAlister triple semigroup over Group([ (1,2) ])>, function( s ) ... end )
gap> T := Range(iso);
<McAlister triple semigroup over Group([ (1,2) ])>
gap> Elements(T);
[ (1, ()), (1, (1,2)), (2, ()) ]
gap> Size(T);
3
gap> IsInjective(iso);
true

I'll look into it.