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On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups
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Alexander N. Skiba
Published/Copyright:
May 30, 2010
Abstract
Let G be a finite group. A subgroup A of G is said to be S-quasinormal in G if AP = PA for all Sylow subgroups P of G. The symbol HsG denotes the subgroup generated by all those subgroups of H which are S-quasinormal in G. A subgroup H is said to be S-supplemented in G if G has a subgroup T such that T ∩ H ⩽ HsG and HT = G; see [Skiba, J. Algebra 315: 192–209, 2007].
Received: 2009-11-03
Published Online: 2010-05-30
Published in Print: 2010-November
© de Gruyter 2010
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Articles in the same Issue
- The power graph of a finite group, II
- On p-Brauer characters of p′-degree and self-normalizing Sylow p-subgroups
- Finite groups whose irreducible characters vanish on at most three conjugacy classes
- The conjugacy of triality subgroups of Sylow subloops of Moufang loops
- On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups
- Periodic patterns in the graph of p-groups of maximal class
- Lower bounds for representation growth
- Reflexive group topologies on Abelian groups
- On abstract commensurators of groups
- On the SQ-universality of groups with special presentations
