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


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
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