### 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 language | English (US) |
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Journal | Bulletin of the London Mathematical Society |

DOIs | |

State | Accepted/In press - 2017 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the London Mathematical Society*. https://doi.org/10.1112/blms.12067

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

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Some conjectures on Frobenius' character sum

AU - Shalev, Aner

AU - Tiep, Pham Huu

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85027512023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027512023&partnerID=8YFLogxK

U2 - 10.1112/blms.12067

DO - 10.1112/blms.12067

M3 - Article

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

ER -