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Finite groups with NE-subgroups
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Yangming Li
Published/Copyright:
May 12, 2006
Abstract
A subgroup H of a finite group G is called an NE-subgroup if it satisfies NG(H) ∩ HG = H, where HG denotes the normal closure of H in G. A finite group G is called a PE-group if every minimal subgroup of G is an NE-subgroup of G. A group G is called a 𝒯-group if every subnormal subgroup of G is normal in G. In this paper, first we give two new characterizations of finite solvable 𝒯-groups in terms of the requirement that certain subgroups are NE-subgroups, and then we obtain new necessary conditions for supersolvability and nilpotency. Finally we classify the finite simple groups all of whose second maximal subgroups are PE-subgroups.
Received: 2004-11-11
Accepted: 2005-01-27
Published Online: 2006-05-12
Published in Print: 2006-01-26
© Walter de Gruyter
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- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
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- Finite groups with NE-subgroups
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Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
