In my homework, an excercise started with the following:
Let $$\alpha = (\alpha_1, \alpha_2) \in Aut(K \times H)$$ (K and H are groups).
My question: shouldn't that be $$ \alpha = (\alpha_1, \alpha_2) \in Aut(K \times H) \times Aut(K \times H)$$?
Later on in the exercise the phrases $\alpha_1(h, k), \alpha_2(h, k)$ appear, so I don't understand how can $\alpha$ be a pair of automorphisms and also an automorphism itself...
Any idea what does it mean? Or is it just a typo of the exercise makers?