Vol. 25, No. 3, 1968

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

Marcel Herzog

Vol. 25 (1968), No. 3, 523–531

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 p-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 NG(M)M,G, then G is isomorphic either to PSL(2,p), m = p > 3, or to PSL(2,m 1), m1 = 2b, b > 1. These results generalize those of R. Brauer, dealing with the case m = p.

Mathematical Subject Classification
Primary: 20.54
Received: 24 April 1967
Published: 1 June 1968
Marcel Herzog