Groups with Prescribed Systems of Schmidt Subgroups

Abstract

A Schmidt (p, q)-group is a Schmidt group G with π(G) = {p, q} and normal Sylow p-subgroup. The N-critical graph ΓNc(G) of a group G is the directed graph with the vertex set π(G) in which (p, q) is an edge iff G has a Schmidt (p, q)-subgroup. The finite groups for which the degrees of vertices of the N-critical graph are at most 2 are studied.