Some conjectures on Frobenius' character sum:

Aner Shalev, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let G be a finite group and let gϵG. In 1896, Frobenius showed that the number of ways to express g as a commutator of elements of G is |G|FG(g), where FG(g)=∑χϵ Irr (G)χ(g)/χ(1) is the Frobenius character sum. This sum received particular attention in the case where G is a (non-abelian) finite simple group, and some related conjectures were posed. In this paper we discuss these conjectures, refute one of them, and provide partial evidence in favor of another one.

Original languageEnglish (US)
Pages (from-to)895-902
Number of pages8
JournalBulletin of the London Mathematical Society
Volume49
Issue number5
DOIs
StatePublished - Oct 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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