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J Hamblin (2007)
Solvable groups satisfying the two-prime hypothesisI. Algebr. Represent. Theory, 10
I. Isaacs, G. Malle, G. Navarro (2007)
A reduction theorem for the McKay conjectureInventiones mathematicae, 170
P. Pálfy (1998)
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M. Lewis, Yanjun Liu (2016)
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James Hamblin, M. Lewis (2007)
Solvable Groups Satisfying the Two-Prime Hypothesis IIAlgebras and Representation Theory, 15
I. Isaacs (1976)
Character Theory of Finite Groups
Let G be a finite group, and write $${\mathrm {cd}}(G)$$ cd ( G ) for the degree set of the complex irreducible characters of G. The group G is said to satisfy the two-prime hypothesis if, for any distinct degrees $$a, b \in {\mathrm {cd}}(G)$$ a , b ∈ cd ( G ) , the total number of (not necessarily different) primes of the greatest common divisor $$\gcd (a, b)$$ gcd ( a , b ) is at most 2. In this paper, we give an upper bound on the number of irreducible character degrees of nonsolvable groups satisfying the two-prime hypothesis and without composition factors isomorphic to $${{\mathrm{PSL}}}_2(q)$$ PSL 2 ( q ) for any prime power q.
Monatshefte f�r Mathematik – Springer Journals
Published: Jul 18, 2016
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