相对存在闭群的零空间
Nullstellensatz for relative existentially closed groups
摘要：
证明了在$G$ -群的每一簇中，每一个$G$ -存在闭元对有限相容方程组都满足零元数.这将推广\cite{BMR1}的{ \bf定理G}。结果我们看到，任意$G$ -群簇中的每对$G$ -存在闭元生成相同的拟簇，如果它们都是$q_ω$ -紧的，则它们是几何等价的.
英文摘要：
We prove that in every variety of $G$-groups, every $G$-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize {\bf Theorem G} of \cite{BMR1}. As a result we see that every pair of $G$-existentially closed elements in an arbitrary variety of $G$-groups generate the same quasi-variety and if both of them are $q_ω$-compact, they are geometrically equivalent.
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