Year: 2026
Type: preprint
Abstract: As an extension of the It^o-Michler theorem to the nonabelian or nonnormal Sylow subgroups, A. Moreto raised the following conjecture: let G be a finite group and P a Sylow p-subgroup of G. Then the number of irreducible characters of G whose degrees are divisible by p is not less than the length of any subgroup chain between N_G(P) and G. In this short note, we give a counterexample to this conjecture.
Source: arXiv (Cornell University)
Authors: Chen, Gang, Zhao, Wenhua
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214085263