Simple groups all of whose second maximal subgroups are (A)-groups (Q1101547)

A subgroup H of a group G is called pronormal in G if H is conjugate to H x in \(<H,H\) \(x>\) for every element x of G. A finite group G is said to be an (A)-group if every subgroup of G of prime order is pronormal in G and either Sylow 2-subgroups of G are abelian or every cyclic subgroup of G of order 4 is pronormal in G. The author classifies the finite groups whose maximal subgroups are (A)-groups. They are solvable. He also proves that a simple finite group all whose second maximal subgroups are (A)- groups is isomorphic to PSL(2,q) for some q.