Baer–Specker group

Baer–Specker group

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.

The group of homomorphisms from the Baer–Specker group to a free abelian group of finite rank is a free abelian group of countable rank.fact|date=September 2008 This provides another proof that the group is not free.

ee also

* Slender group

References

*


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