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Algebra and Discrete Mathematics, 2013, Volume 15, Issue 1, Pages 83–95 (Mi adm413)  

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
References:
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 $S_3$.
Received: 19.10.2011
Revised: 26.06.2012
Bibliographic databases:
Document Type: Article
MSC: 20B30, 08A40,20F12
Language: English
Citation: E. Płonka, “Associative words in the symmetric group of degree three”, Algebra Discrete Math., 15:1 (2013), 83–95
Citation in format AMSBIB
\Bibitem{Plo13}
\by E.~P\l onka
\paper Associative words in the symmetric group of degree three
\jour Algebra Discrete Math.
\yr 2013
\vol 15
\issue 1
\pages 83--95
\mathnet{http://mi.mathnet.ru/adm413}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3100131}
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