MATHEMATICS

Simple non-abelian groups with second maximal pronormal subgroups

V. N. Tyutyanov

International University MITSO, Gomel

Abstract: V.I. Zenkov put in the Kourovskaya notebook the following problem 19.109: is it true that in a non-abelian finite simple group $G$ all maximal subgroups are Hall subgroups if and only if every second maximal subgroup is pronormal in $G$? This paper shows that this problem is solved negatively.

Keywords: finite group, second maximal subgroup, pronormal subgroup.

UDC: 512.542

Received: 12.04.2019