Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters
| Autor: | Neda Ahanjideh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | AUT Journal of Mathematics and Computing, Vol 4, Iss 1, Pp 87-89 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2783-2449 2783-2287 |
| DOI: | 10.22060/ajmc.2022.21894.1119 |
| Popis: | For a character $ \chi $ of a finite group $ G $, the number $ \chi^c(1)=\frac{[G:{\rm ker}\chi]}{\chi(1)} $ is called the co-degree of $ \chi $. Let ${\rm Sol}(G)$ denote the solvable radical of $G$. In this paper, we show that if $G$ is a finite non-solvable group with $\{\chi^c(1)_2:\chi \in {\rm Irr}(G)\}=\{1,2^m\}$ for some positive integer $m$, then $G/{\rm Sol}(G)$ has a normal subgroup $M/{\rm Sol}(G)$ such that $M/{\rm Sol}(G)\cong {\rm PSL}_2(2^n)$ for some integer $n \geq 2$, $[G:M]$ is odd and $ G/{\rm Sol}(G) \lesssim {\rm Aut}({\rm PSL}_2(2^n))$. |
| Databáze: | Directory of Open Access Journals |
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