Let be a non-empty set, and an abelian group. The set of all functions from to is an abelian group, with addition defined elementwise by . The zero element is the function that sends all elements of into of , and the negative of an element is a function defined by .
When , the set of natural numbers, and , as defined above is called the Baer-Specker group. Any element of , being a function from to , can be expressed as an infinite sequence , and the elementwise addition on can be realized as componentwise addition on the sequences:
- 1 P. A. Griffith, Infinite Abelian Group Theory, The University of Chicago Press (1970)