2026/08/04 by Inna Capdeboscq, Chris Parker
Mathematics · #math.GR
A group G is invariably generated by two elements a and b if G=⟨ ag,bh⟩ for all g,h∈ G. This paper provides a structural description of finite groups invariably generated by two elements of distinct prime orders s and t. We illustrate the use of our main result in a case study with s=2 and t=3. In particular we prove that an almost simple group is invariably generated by an element of order 2 and an element of order 3 if and only if it is isomorphic to PGL2(32b) for some b ≥ 1.