Geodesic
Associative words in the symmetric group of degree three
Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 83-95

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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 $S_3$. 
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     author = {E. P{\l}onka},
     title = {Associative words in the symmetric group of degree three},
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E. Płonka. Associative words in the symmetric group of degree three. Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 83-95. http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a7/