Character triples and relative defect zero characters

2024/08/24 by Zhang, Junwei, Wang, Lizhong, Jin, Ping
#20C15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2408.13436

Abstract

Given a character triple (G,N,θ), which means that G is a finite group with N \vartriangleleft G and θ∈\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∈ H²(G/N,ℂ^×) 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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