Let G be $\underbrace{\mathbb Z_p\times\dots\times \mathbb Z_p}_{n \text{ times}}$. Find $A(G)$ (the Automorphism group of $G$).
($\mathbb Z_p$ is the integres modulo p, for example $\mathbb Z_2=\{0,1\},\ \ \mathbb Z_5=\{0,1,2,3,4\}$)
I thoght about:
Think about $(\mathbb Z_p)^n$ as vector space over $\mathbb Z_p$ of dimension n. Then to think about the automorphisms as linear transformations (do I need to explain it more?). So $A(\mathbb Z_p)^n$ is equal to to the space of all invertible linear transformations of $(\mathbb Z_p)^n$ to itself. Then we get that $A(G)\cong GL_n(\mathbb Z_p)$.
is that enough or I need to add something?