Strongly Real Elements in Sporadic Groups and Alternating Groups

Abstract

We determine the elements in the Sporadic and the Alternating Groups which are strongly real. In the Alternating Groups every real element is strongly real, but this is not true in all Sporadic Groups. Main results for the Alternating groups are given in proposition 6 while the results for the Sporadic Groups are computed manually or by using GAP[5]. The Alternating and the Sporadic Groups in which every element is strongly real are A_n for (n = 5, 6, 10, 14), and J₁ and J₂.

Keywords: Finite simple groups, Real elements, Strongly real elements, Complex character.

2000 Mathematics Subject Classification. Primary: 20D06; Secondary: 20F05