University of IsfahanInternational Journal of Group Theory2251-76507320180901Finite groups with non-trivial intersections of kernels of all but one irreducible characters63802160910.22108/ijgt.2017.21609ENMariagraziaBianchiDipartimento di Matematica quot;Federigo Enriques quot;, Università di MilanoMarcelHerzogSchoool of Mathematical Sciences,
Tel-Aviv UniversityJournal Article20160715In 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.https://ijgt.ui.ac.ir/article_21609_42a17a94ecfbfa1359519bb03978b0aa.pdf