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

Document Type : Original Article

Author

Department of pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

Abstract

For a character χ of a finite group G, the number $χc (1)=\frac{[G:ker χ]}{χ(1)} $ is called the co-degree of χ. Let Sol(G) denote the solvable radical of G. In this paper, we show that if G is a finite non-solvable group with {χc(1)2 : χ∈Irr(G)={1,2m} for some positive integer m, then G/Sol(G) has a normal subgroup M/Sol(G) such that M/Sol(G) ≅ PSL2(2n) for some integer n≥2, [G:M] is odd and $G/Sol(G) \lesssim Aut(PSL2(2n)$. 

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