On Huppert’s ρ - σ conjecture for blocks

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Christine Bessenrodt
  • Yang Liu
  • Ziqun Lu
  • Jiping Zhang

External Research Organisations

  • Tianjin Normal University
  • Tsinghua University
  • Peking University
View graph of relations

Details

Original languageEnglish
Pages (from-to)339-347
Number of pages9
JournalArchiv der Mathematik
Volume118
Issue number4
Early online date10 Feb 2022
Publication statusPublished - Apr 2022

Abstract

For n∈ N, we denote by π(n) the set of prime divisors of n. For a block B of a finite group G, let Irr(B) be the set of irreducible complex characters of G belonging to B. Let ρ(B) be the set of those primes dividing the degree of some character in Irr(B), and let σ(B) be the maximal number of primes dividing such a degree. For a solvable group G, we prove that | ρ(B) | ≤ 3 σ(B) + 1. This provides a block result in the spirit of Huppert’s ρ-σ conjecture.

Keywords

    Block, Finite group, Irreducible character

ASJC Scopus subject areas

Cite this

On Huppert’s ρ - σ conjecture for blocks. / Bessenrodt, Christine; Liu, Yang; Lu, Ziqun et al.
In: Archiv der Mathematik, Vol. 118, No. 4, 04.2022, p. 339-347.

Research output: Contribution to journalArticleResearchpeer review

Bessenrodt, C, Liu, Y, Lu, Z & Zhang, J 2022, 'On Huppert’s ρ - σ conjecture for blocks', Archiv der Mathematik, vol. 118, no. 4, pp. 339-347. https://doi.org/10.1007/s00013-021-01696-9
Bessenrodt, C., Liu, Y., Lu, Z., & Zhang, J. (2022). On Huppert’s ρ - σ conjecture for blocks. Archiv der Mathematik, 118(4), 339-347. https://doi.org/10.1007/s00013-021-01696-9
Bessenrodt C, Liu Y, Lu Z, Zhang J. On Huppert’s ρ - σ conjecture for blocks. Archiv der Mathematik. 2022 Apr;118(4):339-347. Epub 2022 Feb 10. doi: 10.1007/s00013-021-01696-9
Bessenrodt, Christine ; Liu, Yang ; Lu, Ziqun et al. / On Huppert’s ρ - σ conjecture for blocks. In: Archiv der Mathematik. 2022 ; Vol. 118, No. 4. pp. 339-347.
Download
@article{a1417dc6653f46d39e41103a5ad463b5,
title = "On Huppert{\textquoteright}s ρ - σ conjecture for blocks",
abstract = "For n∈ N, we denote by π(n) the set of prime divisors of n. For a block B of a finite group G, let Irr(B) be the set of irreducible complex characters of G belonging to B. Let ρ(B) be the set of those primes dividing the degree of some character in Irr(B), and let σ(B) be the maximal number of primes dividing such a degree. For a solvable group G, we prove that | ρ(B) | ≤ 3 σ(B) + 1. This provides a block result in the spirit of Huppert{\textquoteright}s ρ-σ conjecture.",
keywords = "Block, Finite group, Irreducible character",
author = "Christine Bessenrodt and Yang Liu and Ziqun Lu and Jiping Zhang",
note = "Funding Information: The project is supported by NSFC (Grant Nos. 11631011, 11701421, 11871011, and 11871292) and the Science & Technology Development Fund of Tianjin Education Commission for Higher Education (2020KJ010). The first author is grateful to the Beijing International Center for Mathematical Research at Peking University for its support and hospitality. The authors are grateful to the referee for the valuable suggestions and comments. ",
year = "2022",
month = apr,
doi = "10.1007/s00013-021-01696-9",
language = "English",
volume = "118",
pages = "339--347",
journal = "Archiv der Mathematik",
issn = "0003-889X",
publisher = "Birkhauser Verlag Basel",
number = "4",

}

Download

TY - JOUR

T1 - On Huppert’s ρ - σ conjecture for blocks

AU - Bessenrodt, Christine

AU - Liu, Yang

AU - Lu, Ziqun

AU - Zhang, Jiping

N1 - Funding Information: The project is supported by NSFC (Grant Nos. 11631011, 11701421, 11871011, and 11871292) and the Science & Technology Development Fund of Tianjin Education Commission for Higher Education (2020KJ010). The first author is grateful to the Beijing International Center for Mathematical Research at Peking University for its support and hospitality. The authors are grateful to the referee for the valuable suggestions and comments.

PY - 2022/4

Y1 - 2022/4

N2 - For n∈ N, we denote by π(n) the set of prime divisors of n. For a block B of a finite group G, let Irr(B) be the set of irreducible complex characters of G belonging to B. Let ρ(B) be the set of those primes dividing the degree of some character in Irr(B), and let σ(B) be the maximal number of primes dividing such a degree. For a solvable group G, we prove that | ρ(B) | ≤ 3 σ(B) + 1. This provides a block result in the spirit of Huppert’s ρ-σ conjecture.

AB - For n∈ N, we denote by π(n) the set of prime divisors of n. For a block B of a finite group G, let Irr(B) be the set of irreducible complex characters of G belonging to B. Let ρ(B) be the set of those primes dividing the degree of some character in Irr(B), and let σ(B) be the maximal number of primes dividing such a degree. For a solvable group G, we prove that | ρ(B) | ≤ 3 σ(B) + 1. This provides a block result in the spirit of Huppert’s ρ-σ conjecture.

KW - Block

KW - Finite group

KW - Irreducible character

UR - http://www.scopus.com/inward/record.url?scp=85124501343&partnerID=8YFLogxK

U2 - 10.1007/s00013-021-01696-9

DO - 10.1007/s00013-021-01696-9

M3 - Article

AN - SCOPUS:85124501343

VL - 118

SP - 339

EP - 347

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 4

ER -