Zobrazeno 1 - 10 of 66 pro vyhledávání: '"A. S. Romanovskii"'
5
Divisible rigid groups. IV. Definable subgroups
Autor: N. S. Romanovskii
Publikováno v: Algebra i logika. 59:344-366
A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, when treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotie
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e4847672879765b0446a842c94e0ba5
https://doi.org/10.33048/alglog.2020.59.305
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6
On the Universal Theories of Generalized Rigid Metabelian Groups
Autor: N. S. Romanovskii
Publikováno v: Siberian Mathematical Journal. 61:878-883
We prove that studying the universal theories of generalized rigid metabelian groups reduces to those of the pairs $ (A,R) $ , where $ R $ is a commutative integral domain and $ A $ is a nontrivial torsion-free subgroup of the multiplicative group $
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f38281cf7ed9fc6e9d155a5d5ef79639
https://doi.org/10.1134/s0037446620050110
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8
Elementary Equivalence and Direct Product Decompositions of Partially Commutative Groups of Varieties
Autor: N. S. Romanovskii, E. I. Timoshenko
Publikováno v: Siberian Mathematical Journal. 61:538-541
Considering the partially commutative groups of the varieties that include the variety of all length 2 nilpotent groups, we study the questions of factor cancellation in direct products, coincidence of elementary theories, characterization of the gro
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3c484e2d5d945dd5a381fc0849e8d992
https://doi.org/10.1134/s0037446620030167
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9
Metabelian pro-$p$-groups with a single relation
Autor: N. S. Romanovskii
Publikováno v: Algebra i logika. 59:116-122
It is proved that there exist uncountably many nonisomorphic pro-p-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-p-groups. Also we give information on pro-p-groups with a single
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cb1abd23563e4e7c6c5d573bb87b811
https://doi.org/10.33048/alglog.2020.59.107
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