A note on the Zariski topology on groups

2023/12/29 by Gil Goffer, Goffer, Gil, Be’eri Greenfeld +1
Computer Science · Mathematics · #20F05 #20F06 #20F65 #22A15 #54H11 #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2312.17727

openalex publication_date 2023/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the semigroup Zariski topology on a group can be strictly coarser than the group Zariski topology on it, answering a question of Elliott, Jonusas, Mesyan, Mitchell, Morayne, and Peresse.

Related

• A note on intrinsic topologies of groups
• Zariski topologies on groups
• Groups with cofinite Zariski topology and potential density
• Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem
• On discrete Zariski-dense subgroups of algebraic groups