On zeros of irreducible characters lying in a normal subgroup

Nicola Grittini, M. J. Felipe, N. Grittini, V. Sotomayor

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

Abstract

Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that χ(g) ≠ 0 for all irreducible characters χ of G. Such an element is said to be non-vanishing inG. 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.
Lingua originaleEnglish
pagine (da-a)1777-1787
Numero di pagine11
RivistaAnnali di Matematica Pura ed Applicata
Volume199
DOI
Stato di pubblicazionePubblicato - 2020

Keywords

  • Conjugacy classes
  • Normal subgroups
  • Irreducible characters
  • Finite groups

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