Character Codegrees of Maximal Class $p$-groups. Issue 2 (25th June 2020)

• Record Type: Journal Article
• Authors: Croome, Sarah; Lewis, Mark L.
• Is Part Of: Canadian mathematical bulletin =. Volume 63:Issue 2(2020)
• Page Start: 328
• Page End: 334
• Publication Date: 2020-06-25
• Subjects: 20C15, -- 20D15; codegree, -- p-group, -- maximal class; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439519000353
• Languages: English
• ISSNs: 0008-4395

Abstract

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.