On a conjecture of huppert for alternating groups
Copyright policy )On a conjecture of huppert for alternating groups
Let \(G\) be a finite group. Let \(cd(G)\) denote the set of degrees of complex irreducible characters of \(G\). In the paper under review the following result on the alternating group is proved: Let \(n\geq 5\). Suppose that there is a prime \(p\) such that elements of \(cd(A_n)\) are either prime to \(p\) or \(p\)-powers and that some \(p\)-power \(>1\) is in \(cd(A_n)\). Then \(n=5\) and \(p=2,3\) or \(5\), or \(n=6\) and \(p=3\). The above result was proved by \textit{A. Balog, C. Bessenrodt, J. B. Olsson}, and \textit{K. Ono} [J. Lond. Math. Soc., II. Ser. 64, No.~2, 344-356 (2001; see the review Zbl 1018.20008 above)], but in the paper under review a direct and elementary proof is provided.
- University of Hannover Germany
Ordinary representations and characters, degrees of complex irreducible characters, Representations of finite symmetric groups, alternating groups, Arithmetic and combinatorial problems involving abstract finite groups
Ordinary representations and characters, degrees of complex irreducible characters, Representations of finite symmetric groups, alternating groups, Arithmetic and combinatorial problems involving abstract finite groups
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