Existence of Hall normal subgroups in finite groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1974 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 16, pages 817-819 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Romanovskij, A. V.;

doi: 10.1007/bf01148126

Existence of Hall normal subgroups in finite groups

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Abstract

We obtain a necessary and sufficient criterion for the existence of an invariant complement to a nilpotent subgroup contained as a direct factor in one of the maximal subgroups of a given group; we also find a condition for the p-closure of a group, all proper subgroups of which are p-closed, expressed in terms of the degree of one of its nonlinear irreducible characters.

Related Organizations

Francisk Skorina Gomel State University
Belarus

Keywords

Special subgroups (Frattini, Fitting, etc.)

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