Orders of inner-diagonal automorphisms of some simple groups of Lie type

Abstract

AbstractWe refer to the set of element orders of a finite group 𝐺 as the spectrum of 𝐺. For the simple groupsPSLn⁢(q)\mathrm{PSL}_{n}(q),PSUn⁢(q)\mathrm{PSU}_{n}(q),E6⁢(q)E_{6}(q), andE62⁢(q){}^{2}E_{6}(q), we describe the spectra of extensions of these groups by diagonal automorphisms.