Advertisement

Archiv der Mathematik

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

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

  • Mark L. Lewis
  • John K. McVey
  • Alexander Moretó
  • Lucía Sanus
Original paper

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.

Mathematics Subject Classification (2000):

20C15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations