Some conjectures on Frobenius' character sum

Aner Shalev, Pham Huu Tiep

Research output: Contribution to journalArticle

Abstract

Let G be a finite group and let g∈G. 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)=∑χ∈ 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)
JournalBulletin of the London Mathematical Society
DOIs
StateAccepted/In press - 2017

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Character Sums
Frobenius
Finite Simple Group
Commutator
Finite Group
Express
Partial
Evidence

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Some conjectures on Frobenius' character sum. / Shalev, Aner; Tiep, Pham Huu.

In: Bulletin of the London Mathematical Society, 2017.

Research output: Contribution to journalArticle

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