Groups with few $p'$-character degrees in the principal block
Representation Theory
2020-04-23 v1
Abstract
Let p be a prime larger than 3 and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct character degrees relatively prime to p in the principal p-block of G. This generalizes a theorem of Isaacs-Smith, as well as a recent result of three of the present authors.
Cite
@article{arxiv.2004.10261,
title = {Groups with few $p'$-character degrees in the principal block},
author = {Eugenio Giannelli and Noelia Rizo and Benjamin Sambale and A. A. Schaeffer Fry},
journal= {arXiv preprint arXiv:2004.10261},
year = {2020}
}
Comments
13 pages; to appear in Proc. AMS