Groups with elementary Abelian centralizers of involutions

An involution $i$ of a group $G$ is said to be almost perfect in $G$ if any two involutions of $i^G$ the order of a product of which is infinite are conjugated via a suitable involution in $i^G$. We generalize a known result by Brauer, Suzuki, and Wall concerning the structure of finite groups with elementary Abelian centralizers of involutions to groups with almost perfect involutions.