具有有限秩的无扭阿贝尔群的结构

The structure of the torsion-free Abelian group with finite rank

通过对有限秩的无扭阿贝尔群的商群的讨论，得出了对有限秩的无扭阿贝尔群的结构的一种刻划即：设G为有限秩的无扭阿贝尔群，G是非p可除的（p为素数），那么存在着子群G*，使得（1）G*为自由阿贝尔群；（2）G／G*为周期群，且G／G*为p可除群；（3）G／G*的每个准素分支均为有限个循环群与拟循环群的直和．且其中关于素数p的准素分支为有限个拟循环群的直和.

A wsv to discribe the structure of a torsion-free abelian group with finite rank is found by studying its quotient group. Let G be a torsion-free abelian group with finite rank, not P-divisible where is a prime. Then there exists a subgroup G* of G/G. are the direct sum of finitely many cyclic and quasicyclic groups, and the p primary component is the sum of finitely many quasicyclic groups.