Invariant class sizes and solvability of finite groups under coprime action

DOI10.1002/MANA.201400363zbMath1348.20019OpenAlexW1908537326WikidataQ59255708 ScholiaQ59255708MaRDI QIDQ2792248

Changguo Shao, Antonio Beltrán Felip

Publication date: 8 March 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201400363

zbMATH Keywords

conjugacy classesfinite \(p\)-groupssolvabilityfinite simple groupsfinite nilpotent groupscoprime actionsconjugacy class sizesprime power order elements

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15)

Related Items (1)

Second maximal invariant subgroups and solubility of finite groups

Cites Work

• Unnamed Item
• On the length of the conjugacy classes of finite groups
• Character theory of finite groups
• Actions with nilpotent fixed point subgroup
• The theory of finite groups. An introduction.
• Notes on the length of conjugacy classes of finite groups.
• On a graph associated to invariant conjugacy classes of finite groups.
• Groups with some arithmetic conditions on real class sizes.
• The characterization of finite groups with abelian Sylow 2-subgroups

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