Associative words in the symmetric group of degree three

• Date: 2018
• Main Author: Plonka, Ernest
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: associative words; symmetric group \(S_3\); 20B30; 08A40,20F12
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/736
• Journal Title: Algebra and Discrete Mathematics

Let G be a group. An element \(w(x,y)\) of the absolutely free group on  free generators \(x,y\) is called an associative word in \(G\) if the equality \(w(w(g_1,g_2),g_3)=w(g_1,w(g_2,g_3))\) holds for all \(g_1,g_2 \in G\). In this paper we determine all associative words in the symmetric group  on...