Further Rigid Triples of Classes in $G_2$

Abstract

We establish the existence of two rigid triples of conjugacy classes in the algebraic group $G_2$ in characteristic $5$, complementing results of the second author with Liebeck and Marion. As a corollary, the finite groups $G_2(5^n)$ are not $(2,4,5)$-generated, confirming a conjecture of Marion in this case.

5 pages. To appear in International Journal of Group Theory