Archiv der Mathematik

, Volume 80, Issue 6, pp 570–577 | Cite as

A graph associated with the $\pi$-character degrees of a group

Original paper


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.

Mathematics Subject Classification (2000):



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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA
  2. 2.Mathematics DepartmentClarion UniversityClarionUSA
  3. 3.Departamento de Matemáticas, Facultad de CienciasUniversidad del País VascoBilbaoSpain
  4. 4.Departament d’AlgebraUniversitat de ValènciaBurjassotSpain

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