Math 417 Homework 8: Due Friday March 28
Instructions: You can discuss these problems with others,
but write up your solutions on your own (i.e., don't just
copy someone else's solutions, else the feedback I give
you won't help you much). Please be neat and write in full sentences.
Do four of the five problems.
-  Problem #30 on p. 131.
-  Problem #38 on p. 132.
-  Problem #10 on p. 145.
-  Problem #12 on p. 145.
-  Let G be the set of all infinite sequences of integers (a1, a2, ... )
which have only finitely many nonzero entries. (Thus every element of G is a sequence
whose entries are integers, and those integers are all eventually 0.)
- Prove that G is a group under componentwise addition. (I.e.,
if x = (x1, x2, ... ) and y = (y1, y2, ... )
are in G, then x + y = (x1 + y1, x2 + y2, ... ).)
- Let Q+ be the group of positive rational numbers under ordinary
multiplication. Prove that G is isomorphic to Q+.