On finite nonsolvable groups whose cyclic $p$-subgroups of equal order are conjugate

DOI10.55730/1300-0098.3301OpenAlexW4295065988MaRDI QIDQ5045145

Robert W. van der Waall, Sezgin Sezer

Publication date: 4 November 2022

Published in: Turkish Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.55730/1300-0098.3301

zbMATH Keywords

conjugacy classesFrattini subgroups\(p\)-subgroupsautomorphism groupsgroups of Lie typeSchur multiplierHering's theoremalternating and symmetric groups(generalized) fitting subgroups(semi-)direct product of groupssporadic simplegroups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Simple groups: sporadic groups (20D08) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Subgroup theorems; subgroup growth (20E07) Special subgroups (Frattini, Fitting, etc.) (20D25) Series and lattices of subgroups (20D30) Automorphism groups of groups (20F28) Finite nilpotent groups, (p)-groups (20D15) Simple groups: alternating groups and groups of Lie type (20D06) Derived series, central series, and generalizations for groups (20F14) Products of subgroups of abstract finite groups (20D40)

Cites Work

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• On the existence of a complement for a finite simple group in its automorphism group
• On automorphisms of finite simple Chevalley groups
• The classification of the finite groups whose supersolvable (nilpotent) subgroups of equal order are conjugate.
• Groups of prime power order. Vol. 3.
• Non-solvable finite groups whose subgroups of equal order are conjugate
• The order of a group of even order
• The orders of the classical simple groups

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