Restrictions on maximal invariant subgroups implying solvability of finite groups

DOI10.1007/s10231-018-0777-1zbMath1446.20030OpenAlexW2883476139WikidataQ129457033 ScholiaQ129457033MaRDI QIDQ1736329

Changguo Shao, Antonio Beltrán Felip

Publication date: 26 March 2019

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-018-0777-1

zbMATH Keywords

nilpotent groupfinite groupsoluble groupcoprime actionmaximal subgroupsupersoluble groupgroup action on groups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Finite nilpotent groups, (p)-groups (20D15)

Related Items (10)

Some generalizations of Shao and Beltrán’s theorem ⋮ Indices of maximal invariant subgroups and solvability of finite groups ⋮ New conditions on maximal invariant subgroups that imply solubility ⋮ Invariant TI-subgroups or subnormal subgroups and structure of finite groups ⋮ On finite groups in which some particular maximal invariant subgroups have indices a prime-power ⋮ Second maximal invariant subgroups and solubility of finite groups ⋮ Invariant TI-subgroups and structure of finite groups ⋮ A coprime action version of a solubility criterion of Deskins ⋮ On a paper of Beltrán and Shao about coprime action ⋮ Orbits of maximal invariant subgroups and solvability of finite groups

Cites Work

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• Finite groups with non-nilpotent maximal subgroups.
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• Actions with nilpotent fixed point subgroup
• The theory of finite groups. An introduction.
• On the number of invariant Sylow subgroups under coprime action
• Indices of maximal invariant subgroups and solvability of finite groups
• Endliche Gruppen I

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