On products of 3-paths in finite full transformation semigroups

• Date: 2022
• Main Authors: Imam, A. T., Ibrahim, M. J.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: 3-path; length formular; full transformation; 20M20; 20M05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1770
• Journal Title: Algebra and Discrete Mathematics

Let \(\operatorname{Sing}_{n}\) denotes the semigroup of all singular self-maps of a finite set \(X_n=\lbrace 1, 2,\ldots, n\rbrace\). A map \(\alpha\in \operatorname{Sing}_{n}\) is called a \(3\)-path if there are \(i, j, k\in X_n\) such that \(i\alpha=j\), \(j\alpha=k\) and \(x\alpha = x\) for all...