# Baer–Specker group

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 20K20 [MSN][ZBL]

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 many copies of the additive group of integers $\mathbb{Z}$. Reinhold Baer proved in 1937 that $\mathcal{B}$ is not 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

**How to Cite This Entry:**

Baer–Specker group.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Baer%E2%80%93Specker_group&oldid=35799