On symmetric words in the symmetric group of degree three
DOI:
https://doi.org/10.7146/math.scand.a-14997Abstract
A word $w(x_{1},x_{2},\ldots,x_{n})$ from absolutely free group $F_{n}$ is called symmetric $n$-word in a group $G$, if the equality $w(g_{1},g_{2},\ldots,g_{n})=w(g_{\sigma 1},g_{\sigma 2},\ldots,g_{\sigma n})$ holds for all $g_{1},g_{2},\ldots,g_{n}\in G$ and all permutations $\sigma\in S_{n}$. The set $\mathbf{S}^{(n)}(G)$ of all symmetric $n$-words is a subgroup of $F_{n}$. In this paper the groups of all symmetric $2$-words and $3$-words for the symmetric group of degree 3 are determined.Downloads
Published
2006-09-01
How to Cite
Plonka, E. (2006). On symmetric words in the symmetric group of degree three. MATHEMATICA SCANDINAVICA, 99(1), 5–16. https://doi.org/10.7146/math.scand.a-14997
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