Computing Hall subgroups of finite groups

DOI10.1112/S1461157012001039zbMath1296.20017OpenAlexW2324471349MaRDI QIDQ5169635

Alexander Hulpke, Bettina Eick

Publication date: 11 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s1461157012001039

zbMATH Keywords

algorithmsnumbers of conjugacy classesfinite permutation groupsconjugacy classes of Hall subgroupsfinite matrix groups

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Software, source code, etc. for problems pertaining to group theory (20-04) Subgroups of symmetric groups (20B35)

Uses Software

• GAP

Cites Work

• On the number of classes of conjugate Hall subgroups in finite simple groups.
• Sylow's theorem in polynomial time
• Hall subgroups of order not divisible by 3
• Computing Sylow subgroups in permutation groups
• Automorphism group computation and isomorphism testing in finite groups
• Odd order Hall subgroups of the classical linear groups
• Solvability of groups of odd order
• Computing subgroups of bounded index in a finite group.
• Constructive Sylow theorems for the classical groups.
• Some remarks on the computation of complements and normalizers in soluble groups
• Special polycyclic generating sequences for finite soluble groups.
• Theorems Like Sylow's
• Finding Sylow normalizers in polynomial time
• Conjugacy classes in finite permutation groups via homomorphic images
• Conjugacy of Odd order Hall Subgroups
• Hall subgroups of the symmetric groups
• Endliche Gruppen I
• Computing the subgroups of a permutation group