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 originale | English |
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pagine (da-a) | 1777-1787 |
Numero di pagine | 11 |
Rivista | Annali di Matematica Pura ed Applicata |
Volume | 199 |
DOI | |
Stato di pubblicazione | Pubblicato - 2020 |
Keywords
- Conjugacy classes
- Finite groups
- Irreducible characters
- Normal subgroups