STRONGLY REAL ELEMENTS IN SPORADIC GROUPS AND ALTERNATING GROUPS

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 J_1 and J_2.