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- Title
Almost simple groups with no product of two primes dividing three character degrees.
- Authors
Aziziheris, Kamal; Ahmadpour, Mohammad
- Abstract
Let Irr(G) denote the set of complex irreducible characters of a finite group G, and let cd(G) be the set of degrees of the members of Irr(G) . For positive integers k and l, we say that the finite group G has the property 𝒫kl if, for any distinct degrees a1, a2, . . . , ak ∈ cd(G), the total number of (not necessarily different) prime divisors of the greatest common divisor gcd(a1, a2, . . . , ak) is at most l−1. In this paper, we classify all finite almost simple groups satisfying the property 𝒫32. As a consequence of our classification, we show that if G is an almost simple group satisfying 𝒫32, then |cd(G)| ⩽ 8.
- Subjects
FINITE simple groups; FINITE groups; GROUP products (Mathematics); DIVISOR theory; CHARACTER
- Publication
Journal of Group Theory, 2019, Vol 22, Issue 5, p865
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0188