TY - JOUR ID - 4993 TI - Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters JO - AUT Journal of Mathematics and Computing JA - AJMC LA - en SN - 2783-2449 AU - Ahanjideh, Neda AD - Department of pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran Y1 - 2023 PY - 2023 VL - 4 IS - 1 SP - 87 EP - 89 KW - The co-degree of a character KW - non-solvable groups KW - irreducible character degrees DO - 10.22060/ajmc.2022.21894.1119 N2 - 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))$. UR - https://ajmc.aut.ac.ir/article_4993.html L1 - https://ajmc.aut.ac.ir/article_4993_0a9857600ac28625b7b6368698f45ead.pdf ER -