Symmetric generating set of the groups Akn + and Skn + 1

Abstract EN

In this paper we will show how to generate in general A^ + , and Skn + l- the alternating and the symmetric groups of degrees kn + 1 -using a copy of S„ and an element of order k + 1 in Akn + , and Skn + , for all positive integers n a 2 and k > 2.

We will also show how to generate Akn + , and Skn + , symmetrically using n elements each of order k + 1.