A graph associated with the p\pi-character degrees of a group |
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Authors: | Mark L Lewis John K McVey Alexander Moretó and Lucía Sanus |
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Institution: | (1) Department of Mathematical Sciences, Kent State University, 44242 Kent, OH, USA;(2) Mathematics Department, Clarion University, 16214 Clarion, PA, USA;(3) Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, 48080 Bilbao, Spain;(4) Departament dAlgebra, Universitat de València, 46100 Burjassot, València, Spain |
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Abstract: | Let G be a group and $\pi$ be a set of primes. We consider the set ${\rm cd}^{\pi}(G)$ of
character degrees of G that are divisible only by primes in $\pi$. In particular, we define
$\Gamma^{\pi}(G)$ to be the graph whose vertex set is the set of primes dividing degrees in ${\rm cd}^{\pi}(G)$. There is an edge between
p and q if pq divides a degree
$a \in {\rm cd}^{\pi}(G)$. We show that if G is $\pi$-solvable, then
$\Gamma^{\pi}(G)$ has at most two connected components. |
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Keywords: | 20C15 |
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