1) Is (Z14, addition under mod 14) isomorphic to a subgroup of (Z35, addition under mod 35)? Of (Z56, addition under mod 56)?

2) Let f: G --> H

a) Show that if H is abelian and f is one-to-one, then G is abelian.

b) Show that if G is abelian and f is onto, then H is abelian.

c) Show that if f is an isomorphism, then G is abelian iff H is.

3) Let G be the group of nonzero complex numbers under multiplication and let H be the subgroup of GL(2,R) consisting of all matrices of the form:

(a b)

(-b a) (It's one matrix, sorry I don't know how to do that in math formula), where not both a and b are 0. Show that G is isomorphic to H.