Generating triples of involutions of alternating groups (Q1311128)

Mazurov asked the question: Which (known) finite simple groups are generated by three involutions, two of which commute? The answer to this question is known for Chevalley groups of rank 1 and for Chevalley groups over a field of characteristic 2. Here we will prove Theorem 1: The alternating group \(A_ n\) is generated by three involutions \(t\), \(u\), \(v\), the first two of which commute, if and only if \(n \geq 9\) or \(n = 5\).