Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters

	Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters
AUT Journal of Mathematics and Computing
مقاله 10، دوره 4، شماره 1، 2023، صفحه 87-89 اصل مقاله (305.2 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21894.1119
نویسنده
Neda Ahanjideh^*
Department of pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
چکیده
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))$.
کلیدواژه‌ها
The co-degree of a character؛ Non-solvable groups؛ Irreducible character degrees
مراجع

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