On distinct character degrees

Abstract

Berkovich, Chillag and Herzog characterized all finite groups G in which all the nonlinear irreducible characters of G have distinct degrees. In this paper we extend this result showing that a similar characterization holds for all finite solvable groups G that contain a normal subgroup N , such that all the irreducible characters of G that do not contain N in their kernel have distinct degrees.

Finite groups in which distinct nonlinear irreducible characters have distinct codegrees

“…Loukaki [13] extends this result by showing that a similar characterization holds for all finite solvable groups 𝐺 that contain a normal subgroup 𝑁, such that all the irreducible characters of 𝐺 that do not contain 𝑁 in their kernel have distinct degrees. This paper focuses on studying 𝐷 ′ -groups, which are finite groups where distinct nonlinear irreducible complex characters have distinct codegrees.…”

“…Loukaki [13] extends this result by showing that a similar characterization holds for all finite solvable groups G that contain a normal subgroup N , such that all the irreducible characters of G that do not contain N in their kernel have distinct degrees.…”

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

“…Other generalizations of the Berkovich, Chillag and Herzog theorem appeared in the literature. We mention here four such papers: [2] by Berkovich, Isaacs and Kazarin in 1999, [9] by Maria Loukaki in 2007, [3] by Dolfi, Navarro and Tiep in 2013 and [4] by Dolfi and Yadav in 2016.…”