Group characters, permutation actions and sharpness

Kenneth W. Johnson, Eirini Poimenidou

Research output: Contribution to journalArticlepeer-review

Abstract

We extend the work which has appeared in papers on sharp characters and originated with Blichfeldt and Maillet to the Burnside ring of a finite group G. We show that the polynomial whose zeros are the set of marks of non-identity subgroups on a faithful G-set X evaluated at X is an integral multiple of the regular G-set, and deduce a result about the size of a base of X. Further consequences for ordinary group characters are obtained by re-examining Blichfeldt's work and we provide alternative definitions of sharpness. Conjectures are given related to the set of values of a permutation character, and it is proved that for a faithful transitive G-set X certain polynomials (in the Burnside ring) evaluated at X necessarily give G-sets.

Original languageEnglish (US)
Pages (from-to)173-182
Number of pages10
JournalEuropean Journal of Combinatorics
Volume24
Issue number2
DOIs
StatePublished - Feb 2003

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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