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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
Factorization in generalized power series
TL;DR: In this article, the existence of irreducible elements in the ring R((G≤0)) consisting of the generalized power series with non-positive exponents was proved.
Book ChapterDOI
Absolutely rigid systems and absolutely indecomposable groups
Paul C. Eklof,Saharon Shelah +1 more
TL;DR: In this article, it was shown that there are arbitrarily large indecomposable abelian groups, that is, groups that cannot be constructed in any generic extension of a generic extension.
Book ChapterDOI
Existence of rigid-like families of Abelian p-groups
TL;DR: In this article, it was shown that for arbitrarily large λ, there are large families of abelian groups, with only the necessary homomorphisms between them, and that these families can be found in a large number of subgroups.
Journal ArticleDOI
The First Integral Cohomology of Pure Mapping Class Groups
Abstract: It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping class groups to the integers. Moreover, we compute the first integral cohomology group associated to the pure mapping class group of any connected orientable surface of genus at least 2 in terms of the surface's simplicial homology. In order to do this, we show that pure mapping class groups of infinite-genus surfaces split as a semi-direct product.