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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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The Kaplansky test problems for ℵ₁-separable groups
TL;DR: In this article, it was shown that the Kaplansky test problem has negative answers for 1-separable abelian groups of cardinality ε ≥ 1, where ε ≤ 1.
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Poly-separated and Ω-stable nilpotent groups
TL;DR: Theorem 1.1 as mentioned in this paper shows that every poly-π-separated nilpotent group is π-separate, i.e., a group can be decomposed as a central product of a π -torsion group of bounded exponent and a radicable group.
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Existence and uniqueness of classifying spaces for fusion systems over discrete p-toral groups
Ran Levi,Assaf Libman +1 more
TL;DR: In this paper, Bob Oliver’s proof to the context of fusion systems over discrete p-toral groups is generalised, thus positively resolving the analogous questions in p-local compact group theory.
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On maximal subgroups of the multiplicative group of a division algebra
TL;DR: In this paper, the existence of a maximal subgroup in the multiplicative group D ∗ of a division algebra D finite-dimensional over its center F is investigated, and it is shown that if the group has no maximal subgroups, then deg ∗ is not a power of 2 and F ∗ 2 is divisible.
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Transitive and Fully Transitive Groups
Steve Files,Brendan Goldsmith +1 more
TL;DR: In this article, the authors examined how the formation of direct sums of p-groups affects transitivity and full transitivity, and uncovered a far-reaching class of p groups for which transitive and fully transitive transitivity are equivalent.