Black Box Classical Groups

William M. Kantor · Ákos Seress

2001年1月 · American Mathematical Society: Memoirs of the American Mathematical Society 第 708 冊 · American Mathematical Soc.

關於這本電子書

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.