On 2-Closedness of the Rational Numbers in Quasivarieties of Nilpotent Groups

Budkin A. I.

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On 2-Closedness of the Rational Numbers in Quasivarieties of Nilpotent Groups

机译：在尼利斯群体的拟亚胺中的合理数量的2封闭

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The dominion of a subgroup H of a group G in a class M is the set of all elements a 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, a (1),..., a (n) ) 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.

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来源
《Siberian Mathematical Journal》 |2017年第6期|共12页
作者
Budkin A. I.;
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作者单位

Altai State Univ Barnaul Russia;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
quasivariety; nilpotent group; additive group of the rational numbers; dominion; 2-closed group;

机译：QuasiSiges;Nilpotent群体;合理数量的添加剂组;统治;2封闭的群体;

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机译：在尼利斯群体的拟亚胺中的合理数量的2封闭
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On 2-Closedness of the Rational Numbers in Quasivarieties of Nilpotent Groups

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