Black box exceptional groups of Lie type

Details Black box exceptional groups of Lie type Black box exceptional groups of Lie type

2011-12-13

arxiv.org/abs/1112.3000v1

Mathematics

Group Theory

Scientific paper

If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank $>1$, other than any $^2F_4(q)$, over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism. In view of its timing, this algorithm yields an upgrade of all known nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to any group $^2F_4(q)$ or $^2G_2(q)$.

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