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This article is cited in 11 scientific papers (total in 11 papers)
$G$-identities and $G$-varieties
M. G. Amaglobeli, V. N. Remeslennikov
Abstract:
G. Baumslag, A. Myasnikov and Remeslennikov [J. Algebra 219 (1999), no. 1, 16–79; MR1707663 (2000j:14003)] presented the fundamentals of algebraic geometry over a fixed group $G$; in particular, they introduced the concept of a category of $G$-groups. For groups in this category, one can also define the concepts of $G$-identity and $G$-variety. We present the fundamentals of the theory of varieties in the category of $G$-groups, of which the most essential is the concept of the group $V_{n,\mathrm{red}}(G)$ of reduced $G$-identities of rank $n$, which is important for the computation of the coordinate groups for algebraic sets over $G$. We prove that $V_{n,\mathrm{red}}(G)=1$ for all natural numbers $n$ if $G$ is a group that is close to a free or relatively free group for some variety of nilpotent groups of rank not less than the nilpotency class of $G$.
Received: 17.11.1999
Citation:
M. G. Amaglobeli, V. N. Remeslennikov, “$G$-identities and $G$-varieties”, Algebra Logika, 39:3 (2000), 249–272; Algebra and Logic, 39:3 (2000), 141–154
Linking options:
https://www.mathnet.ru/eng/al276 https://www.mathnet.ru/eng/al/v39/i3/p249
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Abstract page: | 281 | Full-text PDF : | 107 | First page: | 1 |
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