RECOGNITION OF THE GROUP E6(2) BY GRUENBERG–KEGEL GRAPH

Abstract

The Gruenberg–Kegel graph (or the prime graph) of a finite group G is a simple graph Γ(G) whose vertices are the prime divisors of the order of G, and two distinct vertices p and q are adjacent in Γ(G) if and only if G contains an element of order pq. A finite group is called recognizable by Gruenberg–Kegel graph if it is uniquely determined up to isomorphism in the class of finite groups by its Gruenberg–Kegel graph. In this paper, we prove that the finite simple exceptional group of Lie type E6(2) is recognizable by its Gruenberg–Kegel graph. © 2021 The authors.