Задача 12.

Write down the partition on left and right cosets of the following groups: a) $\mathbb{Z} / \ 2 \mathbb{Z}$; b) $S_n / \ A_n$; c) $S_3 / \ \langle (1,2) \rangle$, where $\langle (1,2) \rangle$ is the minimal subgroup of $S_3$ that has trasposition $(1,2) = \bigl(\begin{smallmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \end{smallmatrix}\bigr) \ $ in it.