2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158402All nonabelian finite simple groups of rank $n$ over a field of size $q$, with the possible exception of the Ree groups $^2G_2(3^{2e+1})$, have presentations with at most $80 $ relations and bit-length $O(\log n +\log q)$. Moreover, $A_n$ and $S_n$ have presentations with 3 generators$,$ 7 relations and bit-length $O(\log n)$, while $\SL(n,q)$ has a presentation with 7 generators, $2 5$ relations and bit-length $O(\log n +\log q)$.48 pagesGroup TheoryCombinatorics20D06, 20F05 (Primary); 20J06 (Secondary)text