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A note on the Zariski topology on groups

Gil Goffer, Be'eri Greenfeld

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.

A note on the Zariski topology on groups

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.
Paper Structure (3 sections, 5 theorems, 17 equations)

This paper contains 3 sections, 5 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Presentations of groups
  3. Proof of main theorem

Key Result

Theorem 1.2

There exists a countable group $\Gamma$ for which $\mathop{\mathrm{Zar^{+}}}\nolimits(\Gamma) \neq \mathop{\mathrm{Zar}}\nolimits(\Gamma)$.

Theorems & Definitions (12)

  • Theorem 1.2
  • Definition 2.1
  • Lemma 2.2: Greendlinger's lemma
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • proof : Proof of Theorem \ref{['thm:main1']}
  • ...and 2 more