MATHEMATICS

Simple non abelian group with $D_\pi$ Schmidt subgroups

V. N. Tyutyanov^a, P. V. Bychkov<sup>b

a</sup> International Institute of Labor and Social Relations, Gomel
^b F. Scorina Gomel State University, Gomel

Abstract: Let $G$ be a finite simple group, $S$ be its Hall Schmidt $\pi$-subgroup. If $2\in\pi$ then $G$ is not a $D_\pi$-group. If $2\notin\pi$ and $G\notin\{A_n(q),^2 A_n(q)\}$ then $G$ is a $D_\pi$-group.

Keywords: group, subgroup, simple group, Hall Schmidt $\pi$-subgroup, $D_\pi$-group.

UDC: 512.542

Received: 26.01.2012