Abelian Groups

Fuchs, L.

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

Cited by 187 publications

(139 citation statements)

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“…If the former holds, G m is quasi-bounded-dsc. Otherwise, by [3,Theorem 35.6], for every m there exists n > m and L n ≤ G n such that K n = π n [G m ]/L n is a divisible group with infinite rank. Since divisible groups are absolute direct summands, for every m we can find f (m) ∈ N, and L f (m) ≤ G f (m) such that…”

Section: Lemma 34 Let G Be a Non-locally Compact Quasi-p-reduced Grmentioning

confidence: 99%

Abelian pro-countable groups and non-Borel orbit equivalence relations

Malicki

2016

Math. Log. Quart.

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We study topological groups that can be defined as Polish, pro‐countable abelian groups, as non‐archimedean abelian groups or as quasi‐countable abelian groups, i.e., Polish subdirect products of countable, discrete groups, endowed with the product topology. We characterize tame groups in this class, i.e., groups all of whose continuous actions on a Polish space induce a Borel orbit equivalence relation, and relatively tame groups, i.e., groups all of whose diagonal actions α×β induce a Borel orbit equivalence relation, provided that α,β are continuous actions inducing Borel orbit equivalence relations.

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Section: Lemma 34 Let G Be a Non-locally Compact Quasi-p-reduced Grmentioning

confidence: 99%

Abelian pro-countable groups and non-Borel orbit equivalence relations

Malicki

2016

Math. Log. Quart.

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“…(1) For 1 n < ω, we denote by T or n (G) the set of g ∈ G such that ng = 0 (in [3] this is denoted as G[n], cf. p. 4).…”

Section: Proof Clearmentioning

confidence: 99%

“…Consider now the following set of equations: 3 . By (e) above and Fact 39(1)(B) we have d(t n , e) < ζ n+1 , and so by Fact 39(2) the set Ω is solvable in G. Let (d n ) n<ω witness this.…”

Section: First Venuementioning

confidence: 99%

Polish topologies for graph products of groups

Paolini

Shelah

2019

J. London Math. Soc.

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“…The undefined explicitly below notions and notations are in agreement with [5]. For instance, a group G is called balanced projective if the equality Bext( , ) {0} G X = holds for all groups X.…”

Section: Introductionmentioning

confidence: 99%