Character triples and relative defect zero characters
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916368830431232 |
|---|---|
| author | Zhang, Junwei Wang, Lizhong Jin, Ping |
| author_facet | Zhang, Junwei Wang, Lizhong Jin, Ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Character triples and relative defect zero characters Zhang, Junwei Wang, Lizhong Jin, Ping Group Theory 20C15 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. |
| title | Character triples and relative defect zero characters |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2408.13436 |