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Infinite Abelian groups
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The article was published on 1970-01-01 and is currently open access. It has received 2613 citations till now. The article focuses on the topics: Elementary abelian group & Rank of an abelian group.read more
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Journal ArticleDOI
Permutation Complexes for Profinite Groups
TL;DR: In this article, a purely algebraic analogue for profinite groups is developed, which enables us to reveal the connection between finiteness conditions on the cohomology of the group and those on the normalizers of the finite p-subgroups.
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Contraadjusted modules, contramodules, and reduced cotorsion modules
TL;DR: In this paper, it was shown that any p-contraadjusted abelian group is p-adically complete, and any padically separated and complete group is a p-constrained contramodule.
Journal ArticleDOI
On N1-free modules with trivial dual
TL;DR: The existence of an N1-free non-free abelian group has been known for over sixty years; the classic example of such a group is the Baer-Specker group, the cartesian product of countably many copies of the group Z of integers as mentioned in this paper.
Journal ArticleDOI
Slenderness, Completions, and Duality for Primary Abelian Groups
TL;DR: In this article, it was shown that if A is a fixed abelian group with endomorphism ring E, then for any group G, let G * ǫ=Hom(G, A ) and for any E -module M, let M * Ã Ǫ ǔ ǒ ǎ ǝ ǚ ǩ ǡ ǐ nj Ǡ ǧ ǥ Ǟ ǜ ǃ ǁ ǀ Ǜ �
Book ChapterDOI
On the Existence of Rigid ℵ1-Free Abelian Groups of Cardinality ℵ1
Rüdiger Göbel,Saharon Shelah +1 more
TL;DR: An abelian group is said to be ℵ1-free if all its countable subgroups are free as mentioned in this paper and a crucial special case of the main result can be stated immediately.