On symmetric words in the symmetric group of degree three - Plonka, Ernest (MATHEMATICA SCANDINAVICA, 2006)
A word w(x_1,x_2,…,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,…,g_n)=w(g_σ 1,g_σ 2,…,g_σ n) holds for all g_1,g_2,…,g_nG and all permutations σS_n. The set 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.