In this paper,the author studies the factorization of direct product of the finite commutative group Z*n.

Let a finite group G act on a finite commutative group E which is equipped with a G-invariant multiplicative symplectic form.

This paper discusses the relation beween order classification and isomorphic classification, gives some important characteristic properties of a cyclic group with order n and a important property of a p-group with finite order, introduces two factorization method of direct product for commutative p-group with finite order, presents some new problems.

Maximal nilpotent subgroups of linear groups over finite commutative rings;