Symmetric and permutational generating set of the groups Akn+1 and Skn+1 using Sn and an element of order k

Abstract

In this paper we will show how to generate Akn+1 and Skn+1 using a copy of Sn and an element of order k in Akn+1 and Skn+1 respectively, for all positive integers n≥2 and all positive integers k≥2. We will also show how to generate Akn+1 and Skn+1 symmetrically using n elements each of order k, for all n≥2 and all even integers k≥2.