TY - JOUR
T1 - Finite groups with non-trivial intersections of kernels of all but one irreducible characters
AU - Bianchi, Mariagrazia
AU - Herzog, Marcel
N1 - Publisher Copyright:
© 2018 University of Isfahan.
PY - 2018/9
Y1 - 2018/9
N2 - In this paper we consider finite groups G satisfying the following condition: G has two columns in its character table which differ by exactly one entry. It turns out that such groups exist and they are exactly the finite groups with a non-trivial intersection of the kernels of all but one irreducible characters or, equivalently, finite groups with an irreducible character vanishing on all but two conjugacy classes. We investigate such groups and in particular we characterize their subclass, which properly contains all finite groups with non-linear characters of distinct degrees, which were characterized by Berkovich, Chillag and Herzog in 1992.
AB - In this paper we consider finite groups G satisfying the following condition: G has two columns in its character table which differ by exactly one entry. It turns out that such groups exist and they are exactly the finite groups with a non-trivial intersection of the kernels of all but one irreducible characters or, equivalently, finite groups with an irreducible character vanishing on all but two conjugacy classes. We investigate such groups and in particular we characterize their subclass, which properly contains all finite groups with non-linear characters of distinct degrees, which were characterized by Berkovich, Chillag and Herzog in 1992.
KW - Complex characters
KW - Finite groups
UR - http://www.scopus.com/inward/record.url?scp=85040810049&partnerID=8YFLogxK
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AN - SCOPUS:85040810049
SN - 2251-7650
VL - 7
SP - 63
EP - 80
JO - International Journal of Group Theory
JF - International Journal of Group Theory
IS - 3
ER -