No abstract

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the B p characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

Let G be the standard wreath product of a finite abelian group by a 2-closed group (a group having a normal Sylow 2-subgroup). It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for such G.

Abstract. A group is said to be a T-group if all its subnormal subgroups are normal. Let G be a finite solvable T-group. It is shown that the normalizer property holds for G. As a direct consequence of our result, we obtain that the normalizer property holds for finite groups all of whose Sylow subgroups are cyclic.