This article is cited in 2 papers

Mathematical logic, algebra and number theory

On intersections of primary subgroups pairs in finite group with socle $\Omega_{2n}^+(2^m)$

V. I. Zenkov<sup>ab

a</sup> N.N. Krasovskii Institute of Mathematics and Mechanics, S.Kovalevskoi street, 16, 620049, Ekaterinburg, Russia
^b Yeltsin Ural Federal University, Mira street, 19, Ekaterinburg, Russia

Abstract: In theorem 1 for $Soc(G) = \Omega_{2n}^+(2)$, $n \ge 3$ and $S \in Syl_2(G)$ subgroup $min_G(S,S) = \langle S \bigcap S^g | |S \bigcap S^g| is\ minimal \rangle$ is constructed. In theorem 2 it is proved that if $Soc(G) = \Omega_{2n}^+(2^m)$ and for primary subgroups $A$ and $B$ we have $min_G(A,B) \ne 1$, then $m=1$, we can assume that $A$ and $B$ are subgroups of $S \in Syl_2(G)$, $|G:Soc(G)|=2$, involution from $G-Soc(G)$ induces the graph automorphism on $Soc(G)$ and $min_G(S,S)\subseteq A\cap B$.

Keywords: finite group, nilpotent subgroup, intersection of subgroups.

UDC: 512.542

MSC: 13A99

Received June 20, 2017, published June 18, 2018

DOI: 10.17377/semi.2018.15.058