On quantitative structure of symplectic groups

TL;DR

This paper investigates the structure of projective symplectic groups over even fields, showing they are uniquely identified by their order and element order counts, thus contributing to the understanding of finite simple groups.

Contribution

It proves that $PSp_{4}(q)$ groups with even q > 2 are uniquely determined by their order and element order distribution, addressing a problem related to finite simple groups.

Findings

Groups $PSp_{4}(q)$ with even q > 2 are uniquely determined by their order and element order set.

The result connects to Thompson's problem for finite simple groups.

Provides a new characterization of symplectic groups in group theory.

Abstract

The main aim of this article is to study the quantitative structure of projective symplectic groups $PSp_{4}(q)$ with $q>2$ even. Indeed, we prove that the groups $PSp_{4}(q)$ 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.