On the Ree groups ^۲{}G_۲(q) characterized by a size of a conjugacy class

One of the important problem in finite groups theory is group characterization by specific property. Properties, such as element order, the set of element with the same order, etc. In this paper, we prove that Ree group ^۲{}G_۲(q), where q\pm\sqrt{۳q}+۱ is a prime number can be uniquely determined by its order and one conjugacy class size.

Keywords:

conjugacy class , Element order , Prime graph , Ree group