The validity of a Thompson's problem for PSL(4,7)

Document Type : Original Article

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)

2 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

Abstract

Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $.
In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.

Keywords

Main Subjects