MATHEMATICS

On the $SE$-core of subgroups of a finite group

A. N. Skiba

F. Skorina Gomel State University, Gomel

Abstract: We give some conditions under which a finite group belongs to a composition formation containing all finite supersoluble groups. The main results of the papers [20]–[32], [34]–[37] are generalized.

Keywords: finite group, saturated formation, composition formation, Baer-local formation, $p$-nilpotent group, cyclic chief factor, supersoluble subgroup, quasisupersoluble group, $S$-quasinormal subgroup, $S$-supplemented subgroup, $S$-quasinormally embedded subgroup, the $SE$-core of subgroup, Sylow subgroup, the generalized Fitting subgroup, maximal subgroup.

UDC: 512.542

MSC: 20D10, 20D15, 20D20

Received: 01.11.2010

Language: English