On the index complex of a maximal subgroup and the group-theoretic properties of a finite group

Wang Xiaojing; Jiang Lining

doi:10.5269/bspm.v23i1-2.7458

On the index complex of a maximal subgroup and the group-theoretic properties of a finite group

Wang Xiaojing, Jiang Lining^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing University of Civil Engineering and Architecture

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

Abstract

Let G be a finite group, S^p(G);Φ'(G) and Φ₁(G) be generalizations of the Frattini subgroup of G. Based on these characteristic subgroups and using Deskins index complex, this paper gets some necessary and su±cient conditions for G to be a p-solvable, π-solvable, solvable, super-solvable and nilpotent group.

Original language	English
Pages (from-to)	65-72
Number of pages	8
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.5269/bspm.v23i1-2.7458
Publication status	Published - 2005

Keywords

Index complex
Nilpo-tent groups
Solvable groups
Super-solvable groups

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Cite this

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AU - Lining, Jiang

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AB - Let G be a finite group, Sp(G);Φ'(G) and Φ1(G) be generalizations of the Frattini subgroup of G. Based on these characteristic subgroups and using Deskins index complex, this paper gets some necessary and su±cient conditions for G to be a p-solvable, π-solvable, solvable, super-solvable and nilpotent group.

KW - Index complex

KW - Nilpo-tent groups

KW - Solvable groups

KW - Super-solvable groups

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ER -

On the index complex of a maximal subgroup and the group-theoretic properties of a finite group

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Keywords

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