Finitely solvable groups with nilpotent wide subgroups

DOI10.1007/S11253-016-1279-1zbMATH Open1499.20040arXiv1603.06551OpenAlexW3098469624MaRDI QIDQ1729517

Irina Sokhor, V. S. Monakhov

Publication date: 27 February 2019

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Abstract: A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent wide subgroups has the quotient group by its hypercenter with no wide subgroups.

Full work available at URL: https://arxiv.org/abs/1603.06551

zbMATH Keywords

finite solvable groups without wide subgroups

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)

Cites Work

• Title not available (Why is that?)
• Finite Non-abelian Simple Groups Which Contain a Non-trivial Semipermutable Subgroup
• Endliche Gruppen I

Related Items (2)

On finite groups with some conditions on subsets. ⋮ Finite solvable groups containing maximal nilpotent subgroups

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