IsomorphismPermGroup does not work for a group of non-perm transformations

[james-d-mitchell]

Originally reported by: wilfwilson (Bitbucket: wilfwilson, GitHub: wilfwilson)

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I get this behaviour in the released version of Semigroups (2.7.4):

#!gap

gap> T := Semigroup([
> Transformation([1, 3, 2, 1]),
> Transformation([2, 1, 3, 2])]);;
gap> iso := IsomorphismPermGroup(T);
MappingByFunction( <transformation group of degree 4 with 2 generators>
, Group([ (2,3), (1,
2) ]), <Attribute "PermutationOfImage">, function( x ) ... end )
gap> inv := InverseGeneralMapping(iso);;
gap> ForAny(T, x -> (x ^ iso) ^ inv = x);
false
gap> Transformation([2, 1, 3, 2]) ^ iso;
(1,2)
gap> last ^ inv;
Transformation( [ 2, 1 ] )

PermutationOfImage is appropriate to get a permutation representation, but will lose information about the kernel of the transformations. Therefore the inverse function needs to do something more involved than what it does, which seems to be AsTransformation.

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• Bitbucket: https://bitbucket.org/james-d-mitchell/semigroups/issue/152

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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I think this is fixed in the 3.0-Dev branch, I fixed a whole lot of problems with isomorphism a there. Can you double check please?

[james-d-mitchell]

Original comment by wilfwilson (Bitbucket: wilfwilson, GitHub: wilfwilson):

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This bug is still present for me in the tip of 3.0-dev, changeset 539131d

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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Right, this is a real bug, I'll try to fix it today.

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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Resolve Issue #152

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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Resolve Issue #152