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	square roots of rationals SquaringConditionForSquareRootInequality squaring condition for square root inequality SqueezeRule squeeze rule SrinivasaRamanujan Srinivasa Ramanujan SSA SSA StabilityOfTransferFunctionsInTheLaplaceDomain stability of transfer functions in the Laplace domain Stabilizer stabilizer StableFixedPoint stable fixed point StableIsomorphism stable isomorphism StableManifold stable manifold StableManifoldTheorem stable manifold theorem StableMarriageProblem stable marriage problem StableMatrix stable matrix