Character degrees and nilpotence class of finite $p$-groups: An approach via pro-$p$ groups

CHARACTER DEGREES AND NILPOTENCE CLASS OF FINITE p-GROUPS: AN APPROACH VIA PRO-p GROUPS

Let S be a finite set of powers of p containing 1. It is known that for some choices of S, if P is a finite p-group whose set of character degrees is S, then the nilpotence class of P is bounded by some integer that depends on S, while for some other choices of S such an integer does not exist. The sets of the first type are called class bounding sets. The problem of determining the class bound...

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...

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

On Finite Groups With Two Irreducible Character Degrees

Brauer pairs of Camina p - groups of nilpotence class 2

In this paper, we find a condition that characterizes when two Camina p-groups of nilpotence class 2 form a Brauer pair. MSC primary: 20C15