View source for Baer–Specker group

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An example of an infinite [[Abelian group]] which is a building block in the structure theory of such groups.

The Baer–Specker group is the group $\mathcal{B} = \mathbb{Z}^{\mathbb{N}}$ of all integer sequences with [[pointwise addition]], that is, the [[direct product]] of [[countably infinite|countably]] many copies of the additive group of integers $\mathbb{Z}$.  Reinhold Baer proved in 1937 that $\mathcal{B}$ is not [[Free Abelian group|free abelian]], whereas Specker proved in 1950 that every countable subgroup of $\mathcal{B}$ is free abelian. 

Cf. [[Slender group]].

==References==
* Phillip A. Griffith, ''Infinite Abelian group theory'', Chicago Lectures in Mathematics, University of Chicago Press (1970) {{ISBN|0-226-30870-7}}