Generating alternating groups (Q1365126)

The starting point of this paper is the claim that for any non-identity element \(x\) of the alternating group \(A_n\) there is \(y\in A_n\) such that \(\langle x,y\rangle=A_n\), made by \textit{I. M. Isaacs} and \textit{T. Zieschang} [Am. Math. Mon. 102, No. 8, 734-739 (1995; Zbl 0846.20004)]. A proof of this theorem is given here. It uses some lemmas from the aforementioned paper, the Jordan theorem on 3-cycles and a detailed analysis of the behaviour of imprimitivity blocks.