Symmetric and permutational generating set of the groups \(A_{kn+1}\) and \(S_{kn+1}\) using \(S_n\) and an element of order \(k\) (Q1392725)

The author shows how to generate either the symmetric or alternating group (depending whether \(n\) and \(k\) are odd or even) of degree \(kn+1\) using three specific permutations, the first two of which generate a subgroup isomorphic to \(S_n\) and the third of which has order \(k\). This generalizes a result of \textit{A. M. Hammas} [ibid. 21, No. 1, 139-143 (1998; Zbl 0897.20023)] which was the case \(k=2\). As in the paper of Hammas, the author also obtains a ``symmetric generating set'' for the group.