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Commutativity Pattern of Finite Non-Abelian p-Groups Determine Their Orders

Abdollahi, A ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1080/00927872.2011.627075
  3. Publisher: 2013
  4. Abstract:
  5. Let G be a non-abelian group and Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G{set minus}Z(G) as the vertices of ΓG, and join two distinct vertices x and y, whenever xy ≠ yx. Here, we prove that "the commutativity pattern of a finite non-abelian p-group determine its order among the class of groups"; this means that if P is a finite non-abelian p-group such that ΓP ≅ ΓH for some group H, then {pipe}P{pipe} = {pipe}H{pipe}
  6. Keywords:
  7. Graph isomorphism ; Groups with abelian centralizers ; Non-commuting graph ; p-group
  8. Source: Communications in Algebra ; Volume 41, Issue 2 , 2013 , Pages 451-461 ; 00927872 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/00927872.2011.627075#.VkwXlC6Hi-E