Symmetric group S_2 - Knowlpedia

The symmetric group $S_2$ is the group of all bijections of $\{1,\ldots,2\}$ , with composition as multiplication.

Order and normal subgroup

There are 2 permutations: choose the images of the 2 letters successively. Its nonidentity permutation is the transposition (12), so it is cyclic of prime order and simple.

References

J. S. Milne, Group Theory, v4.01, §4, symmetric and alternating groups; Theorem 4.33 and Remark 4.34, p. 69.