Two theorems about equationally noetherian groups

[摘要] An algebraic set over a group G is the set of all solutions of some system {f(x(1),..., x(n)) = 1 \ f is an element of G * [x(1),...x(n)]} Of equations over G. A group G is equationally noetherian if every algebraic set over G is the set of all solutions of a finite subsystem of the given one. We prove that a virtually equationally noetherian group is equationally noetherian and that the quotient of an equationally noetherian group by a normal subgroup which is a finite union of algebraic sets is again equationally noetherian. On the other hand, the wreath product W = U (sic) T of a non-abelian group U and an infinite group T is not equationally noetherian. (C) 1997 Academic Press.

[发布日期] 1997-08-15