A note on element orders and character codegrees. (English) Zbl 1232.20014

Qian, Guohua

Arch. Math. 97, No. 2, 99-103 (2011).

The main result of this paper is: Theorem. Let \(G\) be a finite solvable group

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and let \(g\) be an element of \(G\). Then there exists an irreducible character \(\chi\) of \(G\) with \(\ker(\chi)\cap\langle g\rangle=\{1\}\) and where \(p\) divides \(|G:\ker(\chi)|/\chi(1)\) for any prime divisor

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\(p\) of the order of \(g\).

Reviewer: R. W. van der Waall (Huizen)

MSC:

20C15	Ordinary representations and characters
20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D60	Arithmetic and combinatorial problems involving abstract finite groups
20C20	Modular representations and characters

Keywords:

finite solvable groups; element orders; characters; character degrees

References:

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