Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ(g)=0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups.
On the orders of zeros of irreducible characters / S. Dolfi, E. Pacifici, L. Sanus, P. Spiga. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 321:1(2009), pp. 345-352. [10.1016/j.jalgebra.2008.10.004]
On the orders of zeros of irreducible characters
E. PacificiSecondo
;
2009
Abstract
Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ(g)=0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups.
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