Order Conjecture for non-commuting graph of a group
The following was conjectured by A. Abdollahi, S. Akbari and H. R. Maimani in (Non-commuting graph of a group, Journal of Algebra, 298 (2006) 468-492.)
It was proved that Order Conjecture is true if and only if it is true for all non-abelian solvable finite -groups. By an -group, we mean a group in which the centralizer of every non-central element is abelian.
The order Conjecture has been refuted in the following paper
[*] A. R. Moghaddamfar, On non-commutating graphs, Siberian Math. J. 47 (2006), no. 5, 911-914.
It is mentioned in [*] that the example given in the article is due to M. Isaacs.
|Title||Order Conjecture for non-commuting graph of a group|
|Date of creation||2013-03-22 15:18:53|
|Last modified on||2013-03-22 15:18:53|
|Last modified by||abdollahi (9611)|