Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

We investigate the separation of irreducible characters by blocks at different primes and the covering of irreducible characters by blocks (viewed as sets of characters); these notions are used to prove results on the group structure. The covering of all characters of a group by principal blocks is only possible when already one principal block suffices or the generalized Fitting subgroup has a...

Let G be a finite group and let p prime number. We prove that if $$\chi \in {{{\text {Irr}}}}_{p'}(G)$$ $${\text {Ker}}\chi $$ does not have solvable normal p-complement then there exists $$\psi such (1)>\chi (1)$$ {Ker}}\psi <{\text . This is $$p'$$ -version of classical theorem Broline Garrison. As consequence, we obtain results on p-parts character codegrees.

Suppose that B $B$ is a Brauer p $p$ -block of finite group with defect D $D$ . If exactly contains four ordinary irreducible characters, then we show has order or five, assuming the Alperin–McKay conjecture holds for

We show that if the principal p-block of a finite group G contains exactly 5 irreducible ordinary characters, then Sylow p-subgroup has order 5, 7 or is isomorphic to one non-abelian 2-groups 8.