Alternating group A_3

The alternating group $A_3$ consists of the even permutations of $\{1,\ldots,3\}$ , with composition as multiplication.

Order and simplicity

Its order is $3$ . Its elements are the identity, $(123)$ , and $(132)$ . Thus 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.