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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),
m− 1 = 2b, b > 1. These results generalize those of R. Brauer, dealing with the case
m = p.
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