Symmetric generating set of the groups A2n+1 and S2n+1 using Sn and an element of order two

Abstract

In this paper we will show how to generate in general A2n+1 and S2n+1 using a copy of Sn and an element of order 2 in A2n+1 or S2n+1 for all positive integers n≥2. We will also show how to generate A2n+1 and S2n+1 symmetrically using n elements each of order 2.