Get maximal subgroups of non-generic classical groups

[ssiccha]

We need to test whether the recognition algorithms for classical groups can distinguish them from their maximal subgroups. These are available in Magma. Is there GAP code that can compute or lookup those groups?

If there is no GAP code we can look into using @hulpke's hulpke/mgmconvert (also see this paper.

[hulpke]

Just as an FYI, and to avoid duplication of work, the motivation of the magma translater was exactly the maximal subgroups code, as it contains a lot of delicate case distinctions that would be easy to overlook by hand. I started work (I just made the repository https://github.com/hulpke/maxtrans public), but it is still probably just 1/3 done. The tricky bit is that it uses a lot of Magma functions for forms, that do not have direct GAP analogues. Anyhow, if someone was interested in testing, that would cvertainly be motivation for me to put more effort in it.

[fingolfin]

What functions for forms are those, exactly? There is the forms package for GAP, perhaps it can help?

[hulpke]

@fingolfin Standardizing forms and finding form-defined (e.g. totally singular) subspaces. I am aware of the forms package, and I also partially translated some of the Magma functions used. Besides using different syntax and parameter conventions, the hard work will be to translate between different standardization conventions.

[fingolfin]

@fieker this is also relevant for us, I guess -- perhaps we can hire somebody to help with this? Questions is whom.

[fingolfin]

Just to record this here, too: I had some students implement a lot of this in https://github.com/gap-packages/ClassicalMaximals and this already let to a bunch of bugs in recog being discovered