Details
Original language | English |
---|---|
Pages (from-to) | 339-347 |
Number of pages | 9 |
Journal | Archiv der Mathematik |
Volume | 118 |
Issue number | 4 |
Early online date | 10 Feb 2022 |
Publication status | Published - 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.
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In: Archiv der Mathematik, Vol. 118, No. 4, 04.2022, p. 339-347.
Research output: Contribution to journal › Article › Research › peer review
}
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 -