Year: 2025
Type: article
Abstract: Given a character triple ( G , N , θ ) (G,N,\theta) , which means that 𝐺 is a finite group with N ⊲ G N\vartriangleleft G and θ ∈ Irr ( N ) \theta\in\operatorname{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 ∈ H 2 ( G / N , C × ) [\theta]_{G/N}\in H^{2}(G/N,\mathbb{C}^{\times}) associated with the character triple, and then we 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 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.
Source: Journal of Group Theory
Authors: Junwei Zhang, Lizhong Wang, Ping Jin
Institutions: Shanxi University, Peking University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5880038960, G7574608529
OpenAlex ID: W4407953829