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arXiv · 2408.13436

Character triples and relative defect zero characters

Junwei Zhang·Lizhong Wang·Ping Jin
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Abstract

Given a character triple $(G,N,θ)$, which means that $G$ is a finite group with $N \vartriangleleft G$ and $θ\in{\rm Irr}(N)$ is $G$-invariant, we introduce the notion of a $π$-quasi extension of $θ$ to $G$ where $π$ is the set of primes dividing the order of the cohomology element $[θ]_{G/N}\in H^2(G/N,\mathbb{C}^\times)$ associated with the character triple, and then establish the uniqueness of such an extension in the normalized case. As an application, we use the $π$-quasi extension of $θ$ to construct a bijection from the set of $π$-defect zero characters of $G/N$ onto the set of relative $π$-defect zero characters of $G$ over $θ$. Our results generalize the related theorems of M. Murai and of G. Navarro.

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Junwei Zhang, Lizhong Wang, Ping Jin. 2024-08-24. Character triples and relative defect zero characters. https://arxiv.org/abs/2408.13436

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