This article is cited in 1 paper

MATHEMATICS

Finite groups with given maximal chains of length $\le 3$

D. P. Andreeva, A. N. Skiba

F. Skorina Gomel State University, Gomel

Abstract: A description of a finite group with the property that every its maximal chain of length 3 contains a proper $S$-quasinormal subgroup, and a description of a finite group with the property that every its 3-maximal subgroup is subnormal ($S$-quasinormal) are obtained.

Keywords: Sylow subgroup, Schmidt group, $n$-maximal subgroup, nilpotent group, maximal chain of length $n$, soluble group, $S$-quasinormal subgroup, subnormal subgroup.

UDC: 512.542

Received: 24.03.2011