V. S. Monakhov, I. K. Chirik, “On supersolvability of a finite group with <nobr>$Z$</nobr>-supplements to the normalizers of Sylow subgroups”, PFMT, 2022, Issue 1(50),Pages <nobr>74

MATHEMATICS

On supersolvability of a finite group with $Z$-supplements to the normalizers of Sylow subgroups

V. S. Monakhov^a, I. K. Chirik^b

^a Francisk Skorina Gomel State University
^b University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus, Minsk

Abstract: We study a finite group in which the normalizer of each Sylow subgroup has a Hall supplement with cyclic Sylow subgroups. In particular, it is established that such groups are supersoluble.

Keywords: finite group, Sylow subgroup, normalizer, cyclic subgroup, supplement.

UDC: 512.542

Received: 25.11.2021

DOI: 10.54341/20778708_2022_1_50_74