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arXiv · 2407.10572

Some results on GVZ-groups with two character degrees

Nabajit Talukdar·Kukil Kalpa Rajkhowa
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Abstract

We investigate the finite groups $G$ for which $\chi(1)^{2}=|G:Z(\chi)|$ for all characters $\chi \in Irr(G)$ and $|cd(G)|=2$, where $cd(G)=\{\chi(1)| \chi \in Irr(G)\}$. We call such a group a GVZ-group with two character degrees. We establish bijections between the sets of characters of some groups obtained from a GVZ-group with two character degrees. Additionally we obtain some alternate characterizations of a GVZ-group with two character degrees and we construct a GVZ-group having the character degree set $\{1,p\}$.

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Nabajit Talukdar, Kukil Kalpa Rajkhowa. 2024-07-15. Some results on GVZ-groups with two character degrees. https://arxiv.org/abs/2407.10572

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