What is the order of automorphism of the abelian group $K=c_3 \oplus c_3 \oplus c_3$, where $c_3$ is a cyclic group of order 3.
From the book, I find that $Aut(K)$ is isomorphic to $GL_3(F_3)$. I want to prove this result. Can anyone suggest me some direction to prove the result.
Any elementary abelian additive $p$-group ($p$ prime) is a vector space over $GF(p)$: the addition is the group operation in the group and
$$a\circ x=\underbrace{x+\dots+x}_{a\, \text{ times}}.$$
A map from this group to itself is a group automorphism iff it is a bijective linear map. So the automorphism group is equal to $GL$.