On quantitative structure of symplectic groups

Abstract

The main aim of this article is to study the quantitative structure of projective symplectic groups $PS{p}_4(q)$ with $q>2$ even. Indeed, we prove that the groups $PS{p}_4(q)$ with $q>2$ even are uniquely determined by their orders and the set of the number of elements of the same order. This result links to the well-known J. G. Thompson's problem (1987) for finite simple groups.