Some conjectures on Frobenius' character sum

Aner Shalev, Pham Huu Tiep

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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
Publication statusAccepted/In press - 2017

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ASJC Scopus subject areas

  • Mathematics(all)

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