For a character χ of finite group G, the co-degree is c (1)=[G:kerχ] χ(1). Let p be prime and let e positive integer. In this paper, we first show that if G p-solvable such e+1 ∤χ (1), for every irreducible then p-length not greater than e. Next, study groups satisfying condition 2 does divide co-degrees their characters.

For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langland's classification of all irreducible admissible representations for such groups. Since no...

Recently, a new conjecture on the degrees of the irreducible Brauer characters of a finite group was presented in [16]. In this paper we propose a ’local’ version of this conjecture for blocks B of finite groups, giving a lower bound for the maximal degree of an irreducible Brauer character belonging to B in terms of the dimension of B and well-known invariants like the defect and the number of...