This article is cited in 1 paper

Existence of Hall normal subgroups in finite groups

A. V. Romanovskii

Gomel State University

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.

UDC: 512. 7

Received: 25.03.1974

 English version: Mathematical Notes, 1974, 16:3, 817–819

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