On 2-Closedness of the Rational Numbers in Quasivarieties of Nilpotent Groups
- 作者: Budkin A.1
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隶属关系:
- Altai State University
- 期: 卷 58, 编号 6 (2017)
- 页面: 971-982
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171552
- DOI: https://doi.org/10.1134/S0037446617060064
- ID: 171552
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详细
The dominion of a subgroup H of a group G in a class M is the set of all elements a ∈ G that have equal images under every pair of homomorphisms from G to a group of M coinciding on H. A group H is said to be n-closed in M if for every group G = gr(H, a1,..., an) of M that contains H and is generated modulo H by some n elements, the dominion of H in G (in M) is equal to H. We prove that the additive group of the rational numbers is 2-closed in every quasivariety M of torsion-free nilpotent groups of class at most 3 whenever every 2-generated group of M is relatively free.