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For groups represented as permutations. Group transitivity, rank 3 groups, orbits and suborbits, stablizers, permutation characters, primitivity are all on-topic.

10 votes

Is there a way of canonically labelling permutation groups?

Babai, Codenotti, and Qiao (ICALP 2012 from Babai's homepage, also in Codenotti's thesis) show how to test permutational isomorphism (=conjugacy - but this might be another good phrase to search with) …
Joshua Grochow's user avatar
4 votes

Identifying Subgroups of the Modular Group via Permutation Representations on Cosets

(I wanted to post this a comment on @Will Sawin's answer, but I don't have the rep yet. Also it turned out to be convenient to flesh it out a little longer than comment.) Will's answer assumes that y …
Joshua Grochow's user avatar
3 votes

Can every permutation group be realized as the automorphism group of a graph (acting on a su...

FYI, this result exists in the literature. The two citations I know of are: L. Babai. Representation of permutation groups by graphs. In Combinatorial theory and its applications, I (Proc. Colloq …
Joshua Grochow's user avatar