Generating triples of involutions of alternating groups

String C-group representations of almost simple groups: a survey

“…In 1980, it was asked in the Kourovka Notebook (Problem 7.30) which finite simple groups can be generated by three involutions, two of which commute. This problem was solved by Nuzhin and Mazurov in [43,50,51,52,53]. The groups P SU 4 (3) and P SU 5 (2), although mentioned by Nuzhin as being generated by three involutions, two of which commute, have recently been discovered not to have such generating sets by Martin Macaj and Gareth Jones (personal communication of Jones, checked independently using Magma).…”

On the generation of Coxeter groups and their alternating subgroups by involutions

“…Mazurov asked in [5] whether a finite simple group can be generated by three involutions, two of which commute. Nuzhin proved in [6] that such triples exist for A n if and only if n D 5 or n > 9. Let us mention also that in [2,4], the authors studied the number of elements of order k required to generate A n for k > 3.…”

Chiral polyhedra and finite simple groups

“…In 1980, it was asked in the Kourovka Notebook (Problem 7.30) which finite simple groups have this property. This was solved by Nuzhin and others in : every non‐abelian finite simple group can be generated by three involutions, two of which commute, with the following exceptions: The groups and , although mentioned by Nuzhin as being generated by three involutions, two of which commute, have recently been discovered not to have such generating sets by M. Macaj and G. Jones (personal communication). Thus every finite simple group, apart from the above exceptions, is the automorphism group of an abstract regular polyhedron.…”

“…In 1980, it was asked in the Kourovka Notebook (Problem 7.30) which finite simple groups have this property. This was solved by Nuzhin and others in [25,26,27,28,23]: every non-abelian finite simple group can be generated by three involutions, two of which commute, with the following exceptions:…”