 For a vertex "x" of "T"2 the string "x"0 is the left child of "x" and the string "x"1 is the right child of "x" in "T"2.The group of all automorphisms Aut("T"2) can thus be thought of as the group of all length-preserving permutations "σ" of formula_8 that also respect the "initial segment" relation, that is such that whenever a string "x" is an initial segment of a string "y" then "σ"("x") is an initial segment of "σ"("y").The Grigorchuk group "G" is then defined as the subgroup of Aut("T"2) generated by four specific elements of Aut("T"2)