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Polynomial-time algorithms for finding elements of prime order and Sylow subgroups. (English) Zbl 0604.20001
Author’s summary: Assume that generators are given for a subgroup G of the symmetric group S n of degree n, and that r is a prime dividing |G|. Polynomial-time algorithms are given for finding an element of G of order r, and for finding a Sylow r-subgroup of G if G is simple.
Reviewer: G.Butler

MSC:
20-04Machine computation, programs (group theory)
68Q25Analysis of algorithms and problem complexity
20B35Subgroups of symmetric groups
20D20Sylow subgroups of finite groups, Sylow properties, π-groups, π-structure
20F05Generators, relations, and presentations of groups
20D06Simple groups: alternating groups and groups of Lie type