PRIMITIVITY OF PERFECT RESIDUUM OF PERMUTATION GROUPS

Abstract

In this paper, the construction of permutation groups which include symmetric groups, alternating groups, dihedral groups and the groups generated by the semidirect product (wreath products) of two permutation groups. The perfect residuum of the constructed groups has been obtained and their primitivity status has been investigated which enable us to formulate some results on such properties concerning the groups. A standard computer program, Groups algorithm and programming (GAP) has been employed in enhancing and validating the result obtained.

Keywords: Primitive groups, Perfect Residuum, permutation groups.