[GAP Forum] abelianized of transitive groups

[hulpke at me.com]

Dear Bill, Dear Forum,

> I have a question which is indirectly related to GAP.
> 
> Let G a transitive subgroup of S_n. I need a bound for [G:G'](=#G/G')
> in term of n. Is there theoretical and/or heuristic result in this direction ?

Heuristic: n^2/p (respectively n^2/4 for p=2) occurs for degree p^a and that bound works for all degrees <=31. I don't have a general proof.

> 
> What is the best way to compute [G:G'] ? It seems AbelianInvariants is faster
> than Size(G/DerivedSugroup(G)).

Size(G)/Size(DerivedSubgroup(G));  If you form the quotient inside `Size' you first construct the factor group.

Best,

   Alexander