Thompson’s conjecture for Lie type groups E 7(q)

Abstract

In this article, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type E 7(q). More precisely, we show that every finite group G with the properties Z(G) = 1 and cs(G) = cs(E 7(q)) is necessarily isomorphic to E 7(q), where cs(G) and Z(G) are the set of lengths of conjugacy classes of G and the center of G respectively.