On the Ranks of Finite Simple Groups

Document Type : Original Article

Authors

Ayoub B.M. Basheer

Jamshid Moori

Department of Mathematical Sciences, North-West University (Mafikeng), P Bag X2046, Mmabatho 2735, South Africa.

10.22034/kjm.2016.15511

Abstract

Let $G$ be a finite group and let $X$ be a conjugacy class of $G.$ The rank of $X$ in $G,$ denoted by $rank(G{:}X)$ is defined to be the minimal number of elements of $X$ generating $G.$ In this paper we review the basic results on generation of finite simple groups and we survey the recent developments on computing the ranks of finite simple groups.

Keywords

Conjugacy classes

rank

generation

simple groups

sporadic groups

Subjects

• 20 Group theory and generalizations

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