Presentations of finite simple groups: a computational approach

Abstract

All nonabelian finite simple groups of rank $n$ over a field of size $q$, with the possible exception of the Ree groups ${}^2{G}_2(3^{2e+1})$, 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, $25$ relations and bit-length $O(\log n+\log q)$.

48 pages