Research Article

On G-character tables for normal subgroups

Published in: Quaestiones Mathematicae
Volume 46 , issue 4 , 2023 , pages: 721–743

DOI: 10.2989/16073606.2022.2040633

Author(s): M.J. Felipe Instituto Universitario de Matemática Pura y Aplicada (IUMPA-UPV), Universitat Politècnica de València, Spain , M.D. Pérez-Ramos Universitat de València, Spain , V. Sotomayor Instituto Universitario de Matemática Pura y Aplicada (IUMPA-UPV), Universitat Politècnica de València, Spain

Keywords: 20C15 , 20E45 , 20C05 , Finite groups , group algebra , irreducible characters , normal subgroups , conjugacy classes

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Abstract

Let N be a normal subgroup of a finite group G. From a result due to Brauer, it can be derived that the character table of G contains square submatrices which are induced by the G-conjugacy classes of elements in N and the G-orbits of irreducible characters of N. In the present paper, we provide an alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool to obtain information of N from the character table of G.

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