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 -