Baer-Specker group

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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.

Definition

The Baer-Specker group is the group B = ZN 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.