On direct products of infinite cyclic groups
نویسندگان
چکیده
منابع مشابه
on varietal capability of infinite direct products of groups
recently, the authors gave some conditions under which a direct product of finitely many groups is $mathcal{v}-$capable if and only if each of its factors is $mathcal{v}-$capable for some varieties $mathcal{v}$. in this paper, we extend this fact to any infinite direct product of groups. moreover, we conclude some results for $mathcal{v}-$capability of direct products of infinitel...
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We study properties of a group, abelian group, ring, or monoid B which (a) guarantee that every homomorphism from an infinite direct product ∏ I Ai of objects of the same sort onto B factors through the direct product of finitely many ultraproducts of the Ai (possibly after composition with the natural map B → B/Z(B) or some variant), and/or (b) guarantee that when a map does so factor (and the...
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We consider, for infinite cardinals κ and α ≤ κ+, the group Π(κ,<α) of sequences of integers, of length κ, with non-zero entries in fewer than α positions. Our main result tells when Π(κ,<α) can be embedded in Π(λ,<β). The proof involves some set-theoretic results, one about families of finite sets and one about families of ultrafilters. Partially supported by NSF grant DMS–0070723. Part of thi...
متن کاملIsomorphisms of Direct Products of Finite Cyclic Groups
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1962
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1962-0136655-5