Generation of finite groups of Lie type

Abstract

Let p p be an odd prime and G G a finite group of Lie type in characteristic other than p p . Fix an elementary abelian p p -subgroup of Aut ⁡ ( G ) \operatorname {Aut} (G) . It is shown that in most cases G G is generated by the centralizers of the maximal subgroups of E E . Results are established concerning the notions of layer generation and balance, and the strongly p p -embedded subgroups of Aut ⁡ ( G ) \operatorname {Aut} (G) are determined.