Kantor, William M. Polynomial-time algorithms for finding elements of prime order and Sylow subgroups. (English) Zbl 0604.20001 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 Cited in 2 ReviewsCited in 8 Documents 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 PDF BibTeX XML Cite \textit{W. M. Kantor}, J. Algorithms 6, 478--514 (1985; Zbl 0604.20001) Full Text: DOI OpenURL