Automorphisms of infinite abelian groups
Solution 1:
The automorphism group, as an additive group, of the $p$-adic integers $\mathbb{Z}_p$ is the same as its group of units, which is isomorphic to $\mathbb{Z}_p\times\mathbb{Z}/(p-1)\mathbb{Z}$ for odd primes $p$. So $\mathbb{Z}_3\times\mathbb{Z}/2\mathbb{Z}$ is isomorphic to its own automorphism group.