# Baer-Specker group

From Citizendium

In mathematics, in the field of group theory, the **Baer-Specker group**, or **Specker group** is an example of an infinite Abelian group which is a building block in the structure theory of such groups.

## Contents

## Definition

The Baer-Specker group is the group *B* = **Z**^{N} of all integer sequences with componentwise addition, that is, the direct product of countably many copies of **Z**.

## Properties

Reinhold Baer proved in 1937 that this group is *not* free abelian; Specker proved in 1950 that every countable subgroup of *B* is free abelian.

## See also

## References

- Phillip A. Griffith (1970).
*Infinite Abelian group theory*. University of Chicago Press, 1, 111-112. ISBN 0-226-30870-7.