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Two Theorems about Equationally Noetherian Groups

✍ Scribed by Gilbert Baumslag; Alexei Myasnikov; Vitaly Roman'kov

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
176 KB
Volume
194
Category
Article
ISSN
0021-8693

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✦ Synopsis

An algebraic set over a group G is the set of all solutions of some system Γ„ Ε½ . Β² :4 f x , . . . , x s 1 N f g G) x , . . . , x of equations over G. A group G is equa-

tionally 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 s U X T of a non-abelian group U and an infinite group T is not equationally noetherian.

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