On finite groups containing a CCT-subgroup with a cyclic sylow subgroup

Let G be a finite group containing a CCT-subgroup M. M is called a CCT-subgroup of G if M contains the centralizer in G of each of its nonunit elements and it is also a trivial-intersection subset of G. In this paper the p-blocks of characters of G of full defect are described in detail, under the additional assumption that the Sylow subgroups of M are cyclic and nontrivial. This information yields, under the same conditions, a detailed characterization of the nonexceptional (with respect to M) irreducible characters of G. As an application, it is shown that if G is also perfect, its order is less than qm(m²+3m+2)/2, where m is the order of M and qm is the order of NG(M), and N_G(M) ∆ M, G, then G is isomorphic either to PSL(2; p), m = p > 3, or to PSL(2, m − 1), m − 1 = 2^b > 1. These results generalize those of R. Brauer, dealing with the case m = p.