The 2-characters of a group and the group determinant

Kenneth W. Johnson, Surinder K. Sehgal

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

A new look at Frobenius' original papers on character theory has produced the following: (a) the group determinant determines the group (Formanek-Sibley); (b) the group is determined by the 1-, 2- and 3-characters of the irreducible representations (Hoehnke-Johnson); and (c) pairs of non-isomorphic groups exist with the same irreducible 1- and 2-characters (Johnson-Sehgal). The examples produced in Johnson and Sehgal have large orders but, recently, McKay and Sibley have proved that the ten Brauer pairs of order 256 have the same irreducible 2-characters. It is shown here that the pairs of non-isomorphic groups of order p3, p and odd prime, have the same irreducible 2-characters. Further results are given on the k-characters of the regular representation/rod a shorter proof of the result mentioned in (c) is indicated. A criterion is given which is sufficient for the 3-character of an arbitrary representation to determine the group.

Original languageEnglish (US)
Pages (from-to)623-631
Number of pages9
JournalEuropean Journal of Combinatorics
Volume16
Issue number6
DOIs
StatePublished - Nov 1995

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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