2015
DOI: 10.1216/rmj-2015-45-5-1645
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Prime divisors of irreducible character degrees

Abstract: Abstract. Let G be a finite group. We denote by ρ(G) the set of primes which divide some character degrees of G and by σ(G) the largest number of distinct primes which divide a single character degree of G. We show that |ρ(G)| ≤ 2σ(G)+1 when G is an almost simple group. For arbitrary finite groups G, we show that |ρ(G)| ≤ 2σ(G) + 1 provided that σ(G) ≤ 2.

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Cited by 4 publications
(9 citation statements)
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“…As the last preliminary result we recall the statement of Theorem A in [19], that proves the strengthened ρ-σ conjecture for almost-simple groups.…”
Section: Preliminariesmentioning
confidence: 82%
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“…As the last preliminary result we recall the statement of Theorem A in [19], that proves the strengthened ρ-σ conjecture for almost-simple groups.…”
Section: Preliminariesmentioning
confidence: 82%
“…One might wonder whether the factor 3 is the right one for non-solvable groups, or one should instead keep the factor 2 and add a suitable constant for getting a tighter bound. In a recent paper ( [19]), H. Tong-Viet studies the so-called strengthened ρ-σ conjecture proposed by Manz and Wolf in [16], that is |ρ(G)| ≤ 2σ(G) + 1 for every finite group G. The strengthened ρ-σ conjecture is verified in [19] for all finite almost-simple groups and also for the groups G such that σ(G) ≤ 2.…”
Section: Introductionmentioning
confidence: 94%
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