On the orders of zeros of irreducible characters

By S. Dolfi, E. Pacifici, Lucia Sanus, Pablo Spiga. 2009

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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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5bb6fab3a06839496c566eb120a3485934e824c5