## (2008)

### Abstract

The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence.

### Citations

22 | Merzljakov, Fundamentals of the theory of groups - Kargapolov, I - 1979 |

18 |
Varieties of algebras and algebraic varieties. Categories of algebraic varieties
- Plotkin
- 1997
(Show Context)
Citation Context ...rphism is so complicated, it is natural to consider a less delicate classification. The notion of the geometric equivalence of universal algebras (see [8]), was investigated in 1995 by B. Plotkin. By =-=[9]-=- two finitely generated universal algebras A1 and A2 from some variety Θ are geometrically equivalent if and only if, the first one can be embedded into some direct power of the second and vice versa ... |

18 |
Classification problems for systems of forms and linear mappings
- Sergeichuk
- 1988
(Show Context)
Citation Context ...tion of these groups up to the isomorphism. The problem of classification of the finite dimension nilpotent class 2 Lie algebras over an algebraic closed field up to the isomorphism was considered in =-=[12]-=- and [2]. In [12] this problem was resolved when the dimension of the center of the algebra is not great then 2. In [2] it was proved that the problem of classification of the finite dimension nilpote... |

14 | Algebraic logic, varieties of algebras and algebraic varieties, in
- Plotkin
- 1995
(Show Context)
Citation Context ... If the problem of the classification up to isomorphism is so complicated, it is natural to consider a less delicate classification. The notion of the geometric equivalence of universal algebras (see =-=[8]-=-), was investigated in 1995 by B. Plotkin. By [9] two finitely generated universal algebras A1 and A2 from some variety Θ are geometrically equivalent if and only if, the first one can be embedded int... |

9 |
Geometrical equivalence of algebras
- Berzins
(Show Context)
Citation Context ... equivalent to the classification of the quasi-varieties generated by a single nilpotent group. The classification of the finitely generated abelian groups up to geometric equivalence was achieved in =-=[3]-=-. It was proved that two abelian groups are geometrically equivalent if and only if, for every prime number p the exponents of their corresponding p-Sylow subgroups coincide, and if one of these group... |

7 | Identities in Lie Algebras - Bahturin - 1985 |

3 | Sergeichuk V. Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild
- Belitskii, Lipyanski
(Show Context)
Citation Context ...hese groups up to the isomorphism. The problem of classification of the finite dimension nilpotent class 2 Lie algebras over an algebraic closed field up to the isomorphism was considered in [12] and =-=[2]-=-. In [12] this problem was resolved when the dimension of the center of the algebra is not great then 2. In [2] it was proved that the problem of classification of the finite dimension nilpotent class... |

3 |
Classification of metabelian p-groups, in: Matrix problems
- Sergeichuk
- 1977
(Show Context)
Citation Context ... from our survey, first of all, from the complication of the wild matrix problem. Also in the 1970s, the problem of classification of the nilpotent class 2 pgroups up to isomorphism was considered in =-=[11]-=-. It was proved that this problem can be reduced to the wild matrix problem even when the rank of the center of the groups is equal to 2. It is known that for every nilpotent torsion free group G ther... |

2 |
Reflections on the classification of torsion free nilpotent groups, Group theory, essays for Philip Hall, edited by K.W. Gruenberg and J.E
- Grunewald, Segal
- 1984
(Show Context)
Citation Context ...ated torsion free nilpotent class 2 groups. In the 1970s the research in this area was very active. We can remember [6], [5], auxiliary technical work [10] and others. Achievements were summarized in =-=[4]-=-. A full classification up to isomorphism was established only for finitely generated torsion free nilpotent class 2 groups of Hirsh length 6. Such modest results indicate the complication of the prob... |

2 |
Paare alternierender Formen
- Scharlau
- 1976
(Show Context)
Citation Context ...rticular the classification of the finitely generated torsion free nilpotent class 2 groups. In the 1970s the research in this area was very active. We can remember [6], [5], auxiliary technical work =-=[10]-=- and others. Achievements were summarized in [4]. A full classification up to isomorphism was established only for finitely generated torsion free nilpotent class 2 groups of Hirsh length 6. Such mode... |

1 |
A note of finite generated torsion-free nilpotent groups of class 2
- Grunewald, Scharlau
- 1979
(Show Context)
Citation Context ...ted nilpotent class 2 groups, in particular the classification of the finitely generated torsion free nilpotent class 2 groups. In the 1970s the research in this area was very active. We can remember =-=[6]-=-, [5], auxiliary technical work [10] and others. Achievements were summarized in [4]. A full classification up to isomorphism was established only for finitely generated torsion free nilpotent class 2... |

1 |
Geometrical equivalence of nilpotent torsion free groups
- Tsurkov
(Show Context)
Citation Context ...tent groups geometric equivalence is closely connected with the logic proprieties of groups: two nilpotent groups are geometrically equivalent if and only if, they have the same quasi-identities (see =-=[13]-=-). So classification of nilpotent groups, up to geometric equivalence is an equivalent to the classification of the quasi-varieties generated by a single nilpotent group. The classification of the fin... |