University of Isfahan International Journal of Group Theory 2251-7650 7 3 2018 09 01 Finite groups with non-trivial intersections of kernels of all but one irreducible characters 63 80 21609 10.22108/ijgt.2017.21609 EN Mariagrazia Bianchi Dipartimento di Matematica quot;Federigo Enriques quot;, Università di Milano Marcel Herzog Schoool of Mathematical Sciences, Tel-Aviv University Journal Article 2016 07 15 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. https://ijgt.ui.ac.ir/article_21609_42a17a94ecfbfa1359519bb03978b0aa.pdf