This article is cited in 6 papers

Intersection of conjugate solvable subgroups in symmetric groups

A. A. Baikalov<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: It is proved that for any solvable subgroup $G$ of an almost simple group $S$ with simple socle isomorphic to $A_n$, $n\ge5$, there are elements $x,y,z,t\in S$ such that $G\cap G^x\cap G^y\cap G^z\cap G^t=1$.

Keywords: symmetric group, solvable group, almost simple group.

UDC: 512.542.7

Received: 10.04.2015
Revised: 18.03.2016

DOI: 10.17377/alglog.2017.56.201

 English version: Algebra and Logic, 2017, 56:2, 87–97

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