In any city not within a county, there is hereby created and established retirement systems as alternative systems to those which have been established under the provisions of sections 86.010 to 86.193. Each such system shall be under the management of a board of trustees hereinafter described and shall be known as “The Police Retirement System of (name of city)” and by such name all of its business shall be transacted, all of its funds invested and all of its cash and securities and other property held. The retirement systems so created shall begin operation as of the first day of October, 1957.