Presentations of finite simple groups: a computational approach

Details Presentations of finite simple groups: a computational approach Presentations of finite simple groups: a computational approach

2008-04-09

arxiv.org/abs/0804.1396v1

Mathematics

Group Theory

48 pages

Scientific paper

All 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 $O(\log n +\log q)$.

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