Bug in the default method for IsInverseSemigroup

[wilfwilson]

gap> S := Semigroup([
>   Transformation([1, 1, 1, 2, 1, 5, 3]),
>   Transformation([1, 4, 4, 4, 6, 6, 6])],
> rec(acting := false));;
gap> IsInverseSemigroup(S);
true
gap> S := Semigroup(S, rec(acting := true));;
gap> IsInverseSemigroup(S);
false
gap> S := Semigroup(S, rec(acting := true));;
gap> IsSemigroupWithCommutingIdempotents(S);
false
gap> IsRegularSemigroup(S);
false

The offending line is 692 in gap/attributes/properties.gi:

return NrLClasses(S) = NrRClasses(S) and NrIdempotents(S) = NrRClasses(S)

This condition is certainly necessary for an inverse semigroup, but it is not sufficient, as the above example shows. This can be sorted by additionally checking IsRegularSemigroup(S) in this line.

[james-d-mitchell]

Good catch, lots of bugs found today!

[james-d-mitchell]

Resolved by PR #378