1) Yes, note that where x,y)\mapsto y" alt="\pi_2:S_7\times\mathbb{Z}_7\to\mathbb{Z}_7x,y)\mapsto y" />

2) What do you think? Suppose that then and thus . Thus, if then . The conclusion follows. Does thatactuallywork? (this is an actual "see if you know the material" question)