Difference between revisions of "Baer–Specker group"
From Encyclopedia of Mathematics
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| − | * Phillip A. Griffith ''Infinite Abelian group theory'', Chicago Lectures in Mathematics, University of Chicago Press (1970) ISBN 0-226-30870-7 | + | * Phillip A. Griffith, ''Infinite Abelian group theory'', Chicago Lectures in Mathematics, University of Chicago Press (1970) {{ISBN|0-226-30870-7}} |
Latest revision as of 07:30, 24 November 2023
2020 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://encyclopediaofmath.org/index.php?title=Baer%E2%80%93Specker_group&oldid=54650
Baer–Specker group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Baer%E2%80%93Specker_group&oldid=54650