On a permutability property of subgroups of finite soluble groups

A. Ballester-Bolinches; John Cossey; X. Soler-EscrivÀ

doi:10.1142/S0219199710003798

On a permutability property of subgroups of finite soluble groups

A. Ballester-Bolinches^*, John Cossey, X. Soler-EscrivÀ

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.

Original language	English
Pages (from-to)	207-221
Number of pages	15
Journal	Communications in Contemporary Mathematics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S0219199710003798
Publication status	Published - Apr 2010

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abstract = "The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.",

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AB - The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.

KW - Finite group

KW - Hypercentral embedding

KW - Soluble group

KW - Subnormal subgroup

KW - System normalizer

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On a permutability property of subgroups of finite soluble groups

Abstract

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