Coarse structures on groups defined by conjugations

• Date: 2021
• Main Authors: Protasov, I., Protasova, K.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: coarse structure defined by conjugations; cellularity; FC-group; ultrafilter; 20E45; 54D80
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1737
• Journal Title: Algebra and Discrete Mathematics

For a group \(G\), we denote by \(\stackrel{\leftrightarrow}{G}\) the coarse space on \(G\) endowed with the coarse structure with the base \(\{\{ (x,y)\in G\times G: y\in x^F \} : F \in [G]^{<\omega} \}\), \(x^F = \{z^{-1} xz : z\in F \}\). Our goal is to explore interplays between algebraic...