Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
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引用次数: 0
摘要
作为第三位作者最近定义的广义共巴塞尔群概念的一个常见的非难广义化,我们引入了半广义共巴塞尔群的概念,并开始了对它的全面研究。具体地说,我们给出了这些群在 p-扭转群和有限无扭转秩群情况下的完整特征,证明这些群完全可以用广义有限 p-秩来确定,而且还取决于它们的商模数最大扭转子群。令人惊讶的是,对于 p 阶群,半广义共巴斯群的概念与广义共巴斯群的概念密切相关。
As a common nontrivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically, we give a complete characterization of these groups in the cases of -torsion groups and groups of finite torsion-free rank by showing that these groups can be completely determined in terms of generalized finite -ranks and also depends on their quotients modulo the maximal torsion subgroup. Surprisingly, for -primary groups, the concept of a semi-generalized co-Bassian group is closely related to that of a generalized co-Bassian group.