Geodesic
Character Codegrees of Maximal Class $p$-groups
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 328-334

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/S0008439519000353
Mots-clés : codegree, p-group, maximal class 
Croome, Sarah; Lewis, Mark L. Character Codegrees of Maximal Class $p$-groups. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 328-334. doi: 10.4153/S0008439519000353
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