You need to show that these are the only automorphisms of . Use the fact that automorphisms map generators to generators. Now, what are the generators of ?
This one is mostly a problem with the definitions, I think.
I am asked to prove that is isomorphic to , where is the group of all automorphisms of .
Obviously the identity function is in . The only other automorphism I can come up with is . etc, etc. to finish showing the isomorphism between and .
Are there truly only two members in ? It seems there should be more, but I can't find any.
-Dan
Thank you. I was unaware of that fact. (Edit: It's pretty obvious, actually, now that I've had some time to think about it.) To finish the argument then, since there are only two generators of ( -1 and 1) there are only two automorphisms that are in . Since is a group of two members it must be isomorphic to .
-Dan