Example

Consider the permutation group G = < a, b> where a = (1,2)(3,4) and b = (1,3)(2,4).

Take the following Schreier tree with root 1.

We compute the generators for G₁ as indicated in the theorem.

t2-1at1 = e,	t3-1bt1 = e,	t1-1at2 = e,	t4-1bt2 = e,
t4-1at3 = e,	t1-1bt3 = e,	t3-1at4 = e,	t2-1bt4 = e.

We conclude that G₁ = {e} and |G| = 4.