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Character Codegrees of Maximal Class $p$-groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  25 September 2019

Sarah Croome  and
Mark L. Lewis
Sarah Croome
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States Email: [email protected]@math.kent.edu
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States Email: [email protected]@math.kent.edu
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Abstract

Let $G$ be a $p$-group and let $\unicode[STIX]{x1D712}$ be an irreducible character of $G$. The codegree of $\unicode[STIX]{x1D712}$ is given by $|G:\,\text{ker}(\unicode[STIX]{x1D712})|/\unicode[STIX]{x1D712}(1)$. If $G$ is a maximal class $p$-group that is normally monomial or has at most three character degrees, then the codegrees of $G$ are consecutive powers of $p$. If $|G|=p^{n}$ and $G$ has consecutive $p$-power codegrees up to $p^{n-1}$, then the nilpotence class of $G$ is at most 2 or $G$ has maximal class.

Keywords

codegreep-groupmaximal class

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 328 - 334
Copyright
© Canadian Mathematical Society 2019

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