FINITE SIMPLE GROUPS WITH TWO MAXIMAL SUBGROUPS OF COPRIME ORDERS

In 1962, V. A. Belonogov proved that if a finite group G contains two maximal subgroups of coprime orders, then either G is one of known solvable groups or G is simple. In this short note based on results by M. Liebeck and J. Saxl on odd order maximal subgroups infinite simple groups we determine possibilities for triples (G, H, M), where G is a finite nonabelian simple group, H and M are maximal subgroups of G with (vertical bar H vertical bar, vertical bar M vertical bar) = 1.