On mean values of multiplicative functions on the symmetric group

Mean values of nonnegative multiplicative functions defined on the symmetric group are explored in the paper. The result gives a sharp quantitative upper bound for their Cesàro mean. An approach that originated in number theory is adopted. It can be further applied for mappings defined on general decomposable structures, in particular, for estimating mean values with respect to multiplicative measures defined on additive partitions of a natural number.