Algebra in superextensions of groups, II: cancelativity and centers

• Date: 2018
• Main Authors: Banakh, Taras, Gavrylkiv, Volodymyr
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Superextension; right-topological semigroup; cancelable element; topological center; algebraic center; 20M99; 54B20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/823
• Journal Title: Algebra and Discrete Mathematics

Given a countable group \(X\) we study the algebraic structure of itssuperextension   \(\lambda(X)\). This is a right-topological semigroup consisting of all  maximal linked systems  on \(X\) endowed with the operation   \(\mathcal A\circ\mathcal B=\{C\subset  X:\{x\in X:x^{-1}C\in\mathcal B\}\in\ma...