Abstract

The aim of this work is using the information in the ATLAS of Finite Groups (Wilson et al., 1985) and by developing a program inside the GAP computational system (The GAP computational System , 2010), to determine all Hall π-subgroups for some finite classical simple groups such as some of the finite unitary and finite simplectic simple groups and some of finite simple groups of of Lie type. The structures and permutation representations of the Hall π-subgroups have been found. By using the following theoretical and computational algorithms, we determined the solvable subgroups of large order of the finite non-abelian simple linear groups G = L2(p) = PSL(2, p), for p ≥ 5 and p is a prime number, also their presentations and permutation representations have been found.

Keywords: Maximal subgroup, Solvable, p-nilpotent, Formation