TY - JOUR
T1 - On zeros of irreducible characters lying in a normal subgroup
AU - Felipe, M. J.
AU - Grittini, Nicola
AU - Sotomayor, V.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Conjugacy classes
KW - Finite groups
KW - Irreducible characters
KW - Normal subgroups
KW - Conjugacy classes
KW - Finite groups
KW - Irreducible characters
KW - Normal subgroups
UR - https://publicatt.unicatt.it/handle/10807/188780
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85078744593&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85078744593&origin=inward
U2 - 10.1007/s10231-020-00942-1
DO - 10.1007/s10231-020-00942-1
M3 - Article
SN - 0373-3114
VL - 199
SP - 1777
EP - 1787
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
IS - 5
ER -