A characterization of odd order extensions of the finite projective symplectic groups ${\rm PSp}(4,\,q)$

Abstract

In a recent paper, W. J. Wong characterized the finite projective symplectic groups ${\text {PSp}}(4,q)$ where $q$ is a power of an odd prime integer by the structure of the centralizer of an involution in the center of a Sylow $2$-subgroup of ${\text {PSp}}(4,q)$. In the present paper, finite groups which contain an involution in the center of a Sylow $2$-subgroup whose centralizer has a more general structure than in the ${\text {PSp}}(4,q)$ case are classified by showing them to be odd ordered extensions of ${\text {PSp}}(4,q)$.