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Baer–Specker group

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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