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Non-commuting graph of a group

Abdollahi, A ; Sharif University of Technology | 2006

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jalgebra.2006.02.015
  3. Publisher: 2006
  4. Abstract:
  5. Let G be a non-abelian group and let Z ( G ) be the center of G. Associate a graph ΓG (called non-commuting graph of G) with G as follows: Take G Z ( G ) as the vertices of ΓG and join two distinct vertices x and y, whenever x y ≠ y x. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finite groups such that ΓG ≅ ΓH, then | G | = | H |. Among other results we show that if G is a finite non-abelian nilpotent group and H is a group such that ΓG ≅ ΓH and | G | = | H |, then H is nilpotent. © 2006 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Non-commuting graph ; Finite group
  8. Source: Journal of Algebra ; Volume 298, Issue 2 , 2006 , Pages 468-492 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S002186930600113X