ON THE TYPE OF CONJUGACY CLASSES AND THE SET OF INDICES OF MAXIMAL SUBGROUPS

Let G be a finite group. By MT(G) = (m(1),..., m(k)) we denote the type of conjugacy classes of maximal subgroups of G, which implies that G has exactly k conjugacy classes of maximal subgroups and m(1),..., m(k) are the numbers of conjugates of maximal subgroups of G, where m(1) <= ... <= m(k). In this paper, we give some new characterizations of finite groups by the type of conjugacy classes of maximal subgroups. By pi(t) (G) we denote the set of indices of all maximal subgroups of G. We also investigate the influence of the set of indices of all maximal subgroups on the structure of finite groups.