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Mar 14 at 8:31 history edited tomasz CC BY-SA 4.0
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Mar 14 at 2:20 vote accept tomasz
Mar 14 at 2:20 comment added tomasz @NickGill: Thanks, these remarks helped a lot!
Mar 14 at 1:00 history became hot network question
Mar 13 at 21:59 answer added KhashF timeline score: 3
Mar 13 at 14:28 answer added Sean Eberhard timeline score: 8
Mar 13 at 13:06 comment added Nick Gill If you impose the condition that orders are coprime, then you are asking about maximal semisimple abelian subgroups of $GL_n(F_p)$ -- which is really a question about tori I guess. The maximum order is then $p^n-1$.
Mar 13 at 13:01 comment added Nick Gill For the $GL_n(F_p)$ question, it's possible to have an abelian group $B$ of order $p^{n^2/4}$ if you dont have the requirement that orders are coprime. Just consider matrices which have 1's on the diagonal and 0's everywhere except in the top right quarter of the matrix.
Mar 13 at 1:24 history asked tomasz CC BY-SA 4.0