Michigan State University Modern Algebra Problem Question

write it as tidy as you can. feel appreciate to have a pdf verson. if use any outside sources, please quote

Problem 3.
a) Prove that SL,(R) 1 GL,(R) and that GL(R)/SL,(R) R*. (Hint: consider det)
b) Let S C CX denote the unit circle. Prove that CX/S (R), where is multiplication.
(Hint: consider the modulus 😀
c) Let S C CX denote the unit circle. Prove that R/21Z S. Here 2nZ = (21). (Hint:
consider the map 6: R+S given by y(O) = cit)
Problem 4. Let G be a group and suppose that H IG.
a) If A