Large character degrees of groups of odd order

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

On Finite Groups With Two Irreducible Character Degrees

Nonsolvable Groups All of Whose Character Degrees Are Odd-Square-Free

A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S 6 G 6 Aut(S) for a finite simple group S. More generally, we show that ifG is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups....

affine subgroups of the classical groups and their character degrees

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

Character degrees of p-groups and pro-p groups

In the 1970s, Isaacs conjectured that there should be a logarithmic bound for the length of solvability of a p-group G with respect to the number of different irreducible character degrees of G. So far, there are just a few partial results for this conjecture. In this note, we say that a pro-p group G has property (I) if there is a real number D = D(G) that just depends on G such that for any o...