Sylow's theorem in polynomial time

DOI10.1016/0022-0000(85)90052-2zbMath0573.20022OpenAlexW2047131975WikidataQ56092202 ScholiaQ56092202MaRDI QIDQ1063109

William M. Kantor

Publication date: 1985

Published in: Journal of Computer and System Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0000(85)90052-2

zbMATH Keywords

symmetric groupsolvable groupspolynomial-time algorithmspermutation representationclassification of finite simple groupsSylow p-subgroupsHall \(\pi \) -subgroups

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Finite simple groups and their classification (20D05) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (12)

Constructing normalisers in finite soluble groups ⋮ Parallel algorithms for solvable permutation groups ⋮ On the length of subgroup chains in the symmetric group ⋮ Constructing composition factors for a linear group in polynomial time ⋮ Two-closure of rank \(3\) groups in polynomial time ⋮ Formations of finite groups in polynomial time: \(\mathfrak{F}\)-residuals and \(\mathfrak{F}\)-subnormality ⋮ Constructive Sylow theorems for the classical groups. ⋮ Finite Groups and Complexity Theory: From Leningrad to Saint Petersburg via Las Vegas ⋮ Finding composition factors of permutation groups of degree \(n\leq 10^ 6\) ⋮ Computing Hall subgroups of finite groups ⋮ Computing the composition factors of a permutation group in polynomial time ⋮ Graph isomorphism problem and \(2\)-closed permutation groups

Cites Work

• Permutation representations of the finite classical groups of small degree or rank
• A polynomial bound for the orders of primitive solvable groups
• Isomorphism of graphs of bounded valence can be tested in polynomial time
• Singer-Zyklen in klassischen Gruppen
• The Sylow 2-subgroups of the finite classical groups
• Polynomial-time algorithms for finding elements of prime order and sylow subgroups
• Polynomial-time versions of Sylow's theorem
• Sylow p-Subgroups of the Classical Groups Over Finite Fields with Characteristic Prime to p
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