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Commuting graphs of group algebras

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/00927870902950654
  3. Abstract:
  4. The commuting graph of a ring R, denoted by Γ(R), is a graph of all whose vertices are noncentral elements of R, and 2 distinct vertices x and y are adjacent if and only if xy = yx. In this article we investigate some graph-theoretic properties of Γ (kG), where G is a finite group, k is a field, and 0 ≠ ⌊G⌋ j∈ k. Among other results it is shown that if G is a finite nonabelian group and k is an algebraically closed field, then GΓ (kG) is not connected if and only if ⌊G⌋ = 6 or 8. For an arbitrary field k, we prove that Γ (kG)is connected if G is a nonabelian finite simple group or G' ≠ G" and G"≠ 1
  5. Keywords:
  6. Commuting graph ; Group algebra
  7. Source: Communications in Algebra ; Volume 38, Issue 9 , 2010 , Pages 3532-3538 ; 00927872 (ISSN)
  8. URL: http://www.tandfonline.com/doi/abs/10.1080/00927870902950654