Fully inert subgroups of divisible Abelian groups
Fully inert subgroups of divisible Abelian groups
复制标题
可分阿贝尔群的完全惰性子群
DOI：
10.1515/jgt-2013-0014
复制
发表时间：
2013
影响因子：
0.5
通讯作者：
Simone Virili
中科院分区：
文献类型：
--
作者：
D. Dikranjan;A. Bruno;L. Salce;Simone Virili
如果商(H + φ(H))/H对G的每一个自同态φ都是有限的，则称阿贝尔群G的子群H是完全惰性的。显然，这是完全不变子群、有限子群和有限指标子群概念的一般推广。我们研究了可分阿贝尔群的完全惰性子群，特别是那些在其可分壳内完全惰性的阿贝尔群，称为惰性群。证明了惰性无扭群与有限秩完全可分解齐次群重合，并给出了惰性群在一般情况下的完备描述。这就得到了可分阿贝尔群的完全惰性子群的一个性质。
A subgroup H of an Abelian group G is said to be fully inert if the quotient (H + φ(H))/H is finite for every endomorphism φ of G. Clearly, this is a common generalization of the notions of fully invariant, finite and finite-index subgroups. We investigate the fully inert subgroups of divisible Abelian groups, and in particular, those Abelian groups that are fully inert in their divisible hull, called inert groups. We prove that the inert torsion-free groups coincide with the completely decomposable homogeneous groups of finite rank and we give a complete description of the inert groups in the general case. This yields a characterization of the fully inert subgroups of divisible Abelian groups.