On zeros of irreducible characters lying in a normal subgroup
[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N h...
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Zusammenfassung: | [EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we also study certain arithmetical properties of the G-conjugacy class sizes of the elements of N which are zeros of some irreducible character of G. In particular, if N=G, then new contributions are obtained.
The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). The research of the second author is partially funded by the Istituto Nazionale di Alta Matematica - INdAM. The third author acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The first and third authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovacion y Universidades (Spain).
Felipe Román, MJ.; Grittini, N.; Sotomayor, V. (2020). On zeros of irreducible characters lying in a normal subgroup. Annali di Matematica Pura ed Applicata (1923 -). 199:1777-1789. https://doi.org/10.1007/s10231-020-00942-1
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Malle, G., Navarro, G. |
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