On quantitative structure of small Ree groups (1606.00049v1)

Published 31 May 2016 in math.GR

Abstract: The main aim of this article is to study quantitative structure of small Ree Groups $^{{2}G_{2}(q)$.} Here, we prove that small Ree groups are uniquely determined by their orders and the set of the number of elements of the same order. As a consequence, we give a positive answer to J. G. Thompson's problem for simple groups $^{{2}G_{2}(q)$.}