Equationally Noetherian group
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Contents
Definition
A group is said to be equationally Noetherian if every system of equations over the group involving finitely many variables is equivalent to a finite subsystem.
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
finite group |
Facts
- Inner automorphism group of equationally Noetherian group is equationally Noetherian
- Equationally Noetherian subgroup of finite index implies equationally Noetherian
References
Journal references
Original use
- Algebraic Geometry over Groups I. Algebraic Sets and Ideal Theory by Gilbert Baumslag, Alexei Myasnikov and Vladimir Remeslennikov, Journal of Algebra, ISSN 00218693, Volume 219,Number 1, Page 16 - 79(September 1999): ^{Official gated copy (PDF)}^{More info}