Finite groups with non-trivial intersections of kernels of all but one irreducible characters

Document Type: Ischia Group Theory 2016

Authors

1 Dipartimento di Matematica quot;Federigo Enriques quot;, Università di Milano

2 Schoool of Mathematical Sciences, Tel-Aviv University

Abstract

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.

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