Nullstellensatz for relative existentially closed groups

2021/05/20 by M. Shahryari, Shahryari, Mohammad
Mathematics · #08A99 #20F70 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2105.09520

openalex publication_date 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \citeBMR1. 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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