It's not clear for me how to find the appropriate transversal element in the next example below for an example for $x,y,z$ elements.
Please would someone show this process completely?
2026-03-25 13:55:27.1774446927
Reidemeister-Schreier rewriting process. How to find the appropriate transversal element?
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The group $S_3$ is defined as $\langle a,b \mid a^2 = b^3 = 1, ba = ab^2\rangle$, where $a = (12), b = (123)$.
The elements $ba$ and $ab ^ 2$ are both equal $(23)$. Since there is a homomorphism from $G$ to $G/H = S_3$, the elements $ba$ and $ab ^ 2$ are in the same coset. Therefore, the Schreier representative $ba$ is equal to $ab ^ 2$.