On symmetric words in the symmetric group of degree three

• Autores: E. Plonka
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 99, Nº 1, 2006, págs. 5-16
• Idioma: inglés
• DOI: 10.7146/math.scand.a-14997
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• Resumen

  • A word w(x1,x2,…,xn) from absolutely free group Fn is called symmetric n-word in a group G, if the equality w(g1,g2,…,gn)=w(gσ1,gσ2,…,gσn) holds for all g1,g2,…,gn∈G and all permutations σ∈Sn. The set S(n)(G) of all symmetric n-words is a subgroup of Fn. In this paper the groups of all symmetric 2-words and 3-words for the symmetric group of degree 3 are determined.