On the ranks of Fi22

Abstract

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G:X) to be the minimum number of elements of X generating G. Moori investigated rank(F_i22:X), where X is a conjugacy class of involutions in the Fischer group F_i22. In the present article, we completely determine the ranks of the Fischer group F_i22 by computing rank(F_i22:X), where X is any conjugacy class of F_i22.

Keywords: Fischer group F_i22, rank, generator, sporadic group

Quaestiones Mathematicae 37(2014), 591-600