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Abelian Groups

Part of the Springer Monographs in Mathematics Book Series

DOI: 10.1007/978-3-319-19422-6

ISBN: 978-3-319-19421-9

Publisher: Springer International Publishing - Springer Journals

Jun 12, 2015

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p-Groups with Elements of Infinite Height

Fuchs, László

Pages: 343 –408

[We continue our study of torsion groups concentrating on p-groups (with unspecified prime p) in the general case when the groups contain elements of infinite height. Matters are more subtle here as one has to deal with transfinite heights that are the central concept both in the search for...
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Torsion-Free Groups

Fuchs, László

Pages: 409 –479

[In this chapter we start the discussion of torsion-free groups. First, we deal with general properties along with the finite rank case, and delegate the in-depth theory of torsion-free groups of infinite rank to the next chapter.]
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Torsion-Free Groups of Infinite Rank

Fuchs, László

Pages: 481 –528

[This chapter continues the theme of torsion-free groups, this time for the infinite rank case. There is no shortage of relevant results.]
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Butler Groups

Fuchs, László

Pages: 529 –572

[The theory of Butler groups is one of the most elaborate branches of abelian groups. We devote a whole chapter to its study. This may seem excessive, since Butler groups are very special, but the fact that the results and the methods provide more than a superficial glimpse into a fascinating...
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Mixed Groups

Fuchs, László

Pages: 573 –612

[Mixed groups form the most general class of abelian groups, and traditionally, the main question is to find out how the torsion and torsion-free parts are put together to create a mixed group.]
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Endomorphism Rings

Fuchs, László

Pages: 613 –653

[With an abelian group A one associates the ring EndA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
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Automorphism Groups

Fuchs, László

Pages: 655 –671

[Needless to say, automorphism groups contain in general much less information about the group structure than the endomorphism rings. There is an enormous contrast between torsion and torsion-free groups, perhaps even larger than from the point of view of endomorphism rings. Here again, the case...
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Groups in Rings and in Fields

Fuchs, László

Pages: 673 –706

[The most frequent occurrence of abelian groups, apart from vector spaces, is undoubtedly the groups found in rings and fields. This chapter is devoted to their study.]

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