--- dasimov@earthlink.net wrote:
Let P denote the direct product of countably many copies of the integers Z.
E.g., the set {f: Z+ --> Z | f is a function} under addition of functions.
Puzzle: Is P a free abelian group? Prove your answer.
--Dan
This group is known as the Baer-Specker group. The requested proof is said to be in Reinhold Baer, "Abelian groups without elements of finite order", Duke Mathematical Journal, vol. 3 (1937) pp. 68-122. Perhaps someone with online access could look this up and give us a description, hopefully somewhat more concise that of the original paper. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com