On Representations of some finite simple groups

Abstract

The aim of this research is using the information in the ATLAS of Finite Groups [15] and by developing a program inside the GAP computational system, [16], to determine all Hall π-subgroups for some finite simple groups such as the Alternating , some of the Sporadic simple groups, the projective special linear groups of dimension 2x2 on GF(q), L2(p)=PSL2(p) where p is a prime number less than 100 ,some of the finite unitary and finite simplectic simple groups and some of finite simple groups of Lie type. The structures and permutation representations of the Hall π-subgroups have been found.