TY - JOUR

T1 - Geometrical equivalence of groups

AU - Plotkin, B.

AU - Plotkin, E.

AU - Tsurkov, A.

PY - 1999

Y1 - 1999

N2 - The notion of geometrical equivalence of two algebras, which is basic for this paper, is introduced in [5], [6]. It is motivated in the framework of universal algebraic geometry, in which algebraic varieties are considered in arbitrary varieties of algebras. Universal algebraic geometry (as well as classic algebraic geometry) studies systems of equations and its geometric images, i.e., algebraic varieties, consisting of solutions of equations. Geometrical equivalence of algebras means, in some sense, equal possibilities for solving systems of equations. In this paper we consider results about geometrical equivalence of algebras, and special attention is paied on groups (abelian and nilpotent).

AB - The notion of geometrical equivalence of two algebras, which is basic for this paper, is introduced in [5], [6]. It is motivated in the framework of universal algebraic geometry, in which algebraic varieties are considered in arbitrary varieties of algebras. Universal algebraic geometry (as well as classic algebraic geometry) studies systems of equations and its geometric images, i.e., algebraic varieties, consisting of solutions of equations. Geometrical equivalence of algebras means, in some sense, equal possibilities for solving systems of equations. In this paper we consider results about geometrical equivalence of algebras, and special attention is paied on groups (abelian and nilpotent).

UR - http://www.scopus.com/inward/record.url?scp=0033422443&partnerID=8YFLogxK

U2 - 10.1080/00927879908826679

DO - 10.1080/00927879908826679

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AN - SCOPUS:0033422443

SN - 0092-7872

VL - 27

SP - 4015

EP - 4025

JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -