Polynomial-time algorithms for finding elements of prime order and Sylow subgroups. (English) Zbl 0604.20001

Kantor, William M.

J. Algorithms 6, 478-514 (1985).

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:

20-04	Software, source code, etc. for problems pertaining to group theory
68Q25	Analysis of algorithms and problem complexity
20B35	Subgroups of symmetric groups
20D20	Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20F05	Generators, relations, and presentations of groups
20D06	Simple groups: alternating groups and groups of Lie type

Keywords:

generators; symmetric group; Polynomial-time algorithms; Sylow r-subgroup