Some conjectures on Frobenius' character sum:

Aner Shalev; Pham Huu Tiep

doi:10.1112/blms.12067

Some conjectures on Frobenius' character sum:

Aner Shalev
, Pham Huu Tiep

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	895-902
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	49
Issue number	5
DOIs	https://doi.org/10.1112/blms.12067
State	Published - Oct 2017

Bibliographical note

Publisher Copyright:
© 2017 London Mathematical Society.

Access to Document

10.1112/blms.12067

Cite this

@article{506dabd2d5a04c7fa2c52c8b14a2eae9,

title = "Some conjectures on Frobenius' character sum:",

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.",

author = "Aner Shalev and Tiep, \{Pham Huu\}",

note = "Publisher Copyright: {\textcopyright} 2017 London Mathematical Society.",

year = "2017",

month = oct,

doi = "10.1112/blms.12067",

language = "אנגלית",

volume = "49",

pages = "895--902",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "5",

}

TY - JOUR

T1 - Some conjectures on Frobenius' character sum:

AU - Shalev, Aner

AU - Tiep, Pham Huu

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85027512023

U2 - 10.1112/blms.12067

DO - 10.1112/blms.12067

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85027512023

SN - 0024-6093

VL - 49

SP - 895

EP - 902

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 5

ER -

Some conjectures on Frobenius' character sum:

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this