RESEARCH ARTICLE

Associative words in the symmetric group of degree three

E. Płonka

Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland

Abstract: 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 three letters.

Keywords: associative words, symmetric group $S_3$.

MSC: 20B30, 08A40,20F12

Received: 19.10.2011
Revised: 26.06.2012

Language: English

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