Baer-Specker group: Difference between revisions
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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. | 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. | ||
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==Properties== | ==Properties== | ||
[[Reinhold Baer]] proved in 1937 that this group is ''not'' [[Free abelian group|free abelian]]; Specker proved in 1950 that every countable subgroup of ''B'' | [[Reinhold Baer]] proved in 1937 that this group is ''not'' [[Free abelian group|free abelian]]; Specker proved in 1950 that every countable subgroup of ''B'' is free abelian. | ||
==See also== | ==See also== | ||
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==References== | ==References== | ||
* {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago Press | year=1970 | isbn=0-226-30870-7 | pages=1, 111-112}} | * {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago Press | year=1970 | isbn=0-226-30870-7 | pages=1, 111-112}}[[Category:Suggestion Bot Tag]] | ||
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Latest revision as of 16:01, 15 July 2024
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.