On supersolvability of finite groups with $\Bbb P$-subnormal subgroups

Document Type: Research Paper

Authors

1 Gomel engineering institute of MES of Republic of Belarus

2 Department of Mathematics, Gomel F. Scorina State University

Abstract

In this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which $\Bbb P$-subnormality guarantees supersolvability‎ ‎of the whole group‎.

Keywords

Main Subjects


GAP (2009) Groups, Algorithms and Programming Version 4.4.12. href{http://www.gap-system.org}{www.gap-system.org}.
W. Gaschutz (1979). Lectures on subgroups of Sylow type in finite soluble groups. Notes of Pure Mathematics, Australian National University, Canberra. 11
B. Huppert (1967). Endliche Gruppen I. Berlin, Heidelberg, New York.
V. N. Kniahina and V. S. Monakhov (18 May 2011). Finite groups with $mathbb P$-subnormal 2-maximal subgroups. arxiv.org e-Print, href{http://arxiv.org/pdf/1105.3663.pdf}{arxiv.org/pdf/1105.3663.pdf} archive.
V. N. Kniahina and V. S. Monakhov (18 Nov 2011). Finite groups with $mathbb P$-subnormal primary cyclic subgroups. arxiv.org e-Print archive, href{http://arxiv.org/pdf/1110.4720}{arxiv.org/pdf/1110.4720}.
V. S. Monakhov (1995). Finite groups with a given set of Schmidt subgroups. Math. Notes. 58 (5), 1183-1186
V. T. Nagrebecki (1975). Finite minimal non-supersolvable groups. In Finite groups (Proc. Gomel Sem.)(Russian), Nauka i Tehnika, Minsk. , 104-108
A. F. Vasilyev, T. I. Vasilyeva and V. N. Tyutyanov (2010). On the finite groups of supersoluble type. Sib. Math. J.. 51 (6), 1004-1012