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Abelian GroupsTorsion Groups

Abelian Groups: Torsion Groups [We are now prepared to plunge into an in-depth study of the major classes of abelian groups. Divisible groups have been fully characterized, so we can concentrate on reduced groups. Our discussion begins with the theory of torsion groups. Since a torsion group is a direct sum of uniquely determined p-groups, it is clear that the study of torsion groups reduces immediately to p-groups. This chapter is primarily concerned with p-groups without elements of infinite heights (called separable p-groups), while the next chapter will concentrate on p-groups containing elements of infinite heights.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Abelian GroupsTorsion Groups

Part of the Springer Monographs in Mathematics Book Series
Fuchs, László
Springer Journals — Jun 12, 2015
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44 pages

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-19421-9
Pages
299 –342
DOI
10.1007/978-3-319-19422-6_10
Publisher site
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Abstract

[We are now prepared to plunge into an in-depth study of the major classes of abelian groups. Divisible groups have been fully characterized, so we can concentrate on reduced groups. Our discussion begins with the theory of torsion groups. Since a torsion group is a direct sum of uniquely determined p-groups, it is clear that the study of torsion groups reduces immediately to p-groups. This chapter is primarily concerned with p-groups without elements of infinite heights (called separable p-groups), while the next chapter will concentrate on p-groups containing elements of infinite heights.]

Published: Jun 12, 2015

Keywords: Torsion Complete Groups; Basic Subgroup; Pure Subgroup; Infinite Height; Finite Summand

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