Unexpected error for IsAutomorphismGroup

[PaulaHaehndel]

The documentation about IsAutomorphismGroup( G ) not specifies that the group has to be given in a special respresentation, but IsAutomorphismGroup( G ) returns an error when called for GL(2,5).

Observed behaviour

 IsAutomorphismGroup(GL(2,5));
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `IsAutomorphismGroup' on 1 arguments at /mnt/c/gap-4.11.0/lib/methsel2.g:249 called from
<function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
 called from read-eval loop at *stdin*:99
type 'quit;' to quit to outer loop

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[fingolfin]

Thanks for the report!

I think IsAutomorphismGroup only works for groups in the filter IsGroupOfAutomorphisms (i.e. whose elements are genuine automorphisms, i.e. GAP mappings). This suggests that...

1. for other groups, such as GL(2,5), it should just return false, instead of producing an error;
2. the documentation should be adjusted to make it clear that this is the intended behavior.

I see no good other option; in particular, while every group is automorphism group of some object, not every group (isomorphism class) is the automorphism group of another group (e.g. C_3 isn't). But I know of no efficient computational criterium to check that; also, it doesn't seem like a very useful property to test for.

Ping @hulpke in case he has more insights.

[hulpke]

IsAutomorphismGroup is the property of being the full automorphism group of another group. It is declared only for IsGroupOfAutomorphisms -- that's why there is a "No method found" error.

The documentation (in morpheus.gd) says:

IsAutomorphismGroup
indicates whether G is the full automorphism group of another
group H, this group is given as value of G.

[fingolfin]

Yeah, that's what I thought.

The I think the documentation would be clearer if it explicitly mentioned IsGroupOfAutomorphisms -- after all, GL(d,p) is also the "full automorphism group of another group".

[PaulaHaehndel]

Thanks.
That explains the behaviour and the documentation, thank you both.
I agree that it would be great if the documentation could be a bit more explicit in this point such that someone reading it doesn't need this conversation to understand it :)