Finite groups with non-trivial intersections of kernels of all but one irreducible characters
نویسندگان
1 Dipartimento di Matematica e Fisica, Università degli Studi della Campania "Luigi Vanvitelli"
2 Dipartimento di Matematica e Applicazioni Renato Caccioppoli - Università degli Studi di Napoli Federico II
doi
10.22108/ijgt.2017.21609چکیده
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.
