Order Conjecture for non-commuting graph of a group

The following was conjectured by A. Abdollahi, S. Akbari and H. R. Maimaniin (Non-commuting graph of a group, Journal of Algebra, 298 (2006) 468-492.)

Order Conjecture. If $G$ and $H$ are two non-abelian finite groups with isomorphic non-commuting graphs, then $|G|=|H|$ .

It was proved that Order Conjecture is true if and only if it is true for all non-abelian solvable finite $A C$ -groups.By an $A C$ -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.

单词	OrderConjectureForNoncommutingGraphOfAGroup
释义	Order Conjecture for non-commuting graph of a group The following was conjectured by A. Abdollahi, S. Akbari and H. R. Maimaniin (Non-commuting graph of a group, Journal of Algebra, 298 (2006) 468-492.) Order Conjecture. If $G$ and $H$ are two non-abelian finite groups with isomorphic non-commuting graphs, then $\|G\|=\|H\|$ . It was proved that Order Conjecture is true if and only if it is true for all non-abelian solvable finite $A C$ -groups.By an $A C$ -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.
随便看	polynomials in algebraic systems Polyomino polyomino Polyrectangle polyrectangle Polytope polytope PonsAsinorum pons asinorum PontryaginDuality Pontryagin duality Pop pop Poset poset PosetHeightAndWidth poset height and width PositionVector position vector Positive positive PositiveCone positive cone PositiveDefinite positive definite