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George Havas Leonard H Soicher and Robert A Wilson
Christoph Kohler and Herbert Pahlings
Charles R LeedhamGreen
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algebra Amer assume automorphism group Babai black box black-box group box group characteristic classical groups complement composition factors conjugacy classes conjugate connected component constructive recognition contains coset enumeration cyclic defined denote efa series elementary abelian elements of G endomorphism finite fields finite group finite simple groups given GL(n graph group G group of order Groups and Computation groups of Lie Hence input involution irreducible isomorphic Lemma Let G Lie type Mathematics Subject Classification matrix groups maximal subgroups method minimal normal subgroup module nilpotent nonabelian obtain oracle p-group ParGAP pc group permutation groups permutation representation polycyclic groups polynomial presentation prime probability problem procedure proof Proposition random elements random walk recognition algorithm regular orbits result root subgroup scalar Section semisimple semisimple elements Seress solvable solvable groups Step subgroup of G subspace Theorem 1.1 torus unisingular vector W. M. Kantor