Year: 2018
Type: preprint
Abstract: Let $G$ be a $p$-group and let $χ$ be an irreducible character of $G$. The codegree of $χ$ is given by $|G:\text{ker}(χ)|/χ(1)$. This paper investigates the relationship between the nilpotence class of a group and the inclusion of $p^2$ as a codegree. If $G$ is a finite $p$-group with coclass $2$ and order at least $p^5$, or coclass $3$ and order at least $p^6$, then $G$ has $p^2$ as a codegree. With an additional hypothesis this result can be extended to $p$-groups with coclass $n\ge 3$ and order at least $p^{2n}$.
Source: arXiv (Cornell University)
Authors: Croome, Sarah, Lewis, Mark L.
Institution: Kent State University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2900200731