Some generalizations of slender Abelian groups

Kruchkov, N. I.

doi:10.1007/s10958-008-9179-z

Cited by 2 publications

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed that many interesting groups, including free groups, free abelian groups and torsion-free word-hyperbolic groups, are lch-slender and cmslender and that for abelian groups we recover the usual slender groups. Several types and properties of automatically continuous were studied in [10,24]. Most recently, Corson and Varghese [11] strengthened the connection between slender groups and automatic continuity by showing that a group is lch-slender if it is torsion-free and it does not contain Q or p-adic integers for any p.…”

Section: Introductionmentioning

confidence: 99%

Inverse limit slender groups

Conner¹,

Herfort²,

Kent³

et al. 2021

Preprint

View full text Add to dashboard Cite

Classically, an abelian group G is said to be slender if every homomorphism from the countable product Z N to G factors through the projection to some finite product Z n . Various authors have proposed generalizations to non-commutative groups, resulting in a plethora of similar but not completely equivalent concepts. In the first part of this work we present a unified treatment of these concepts and examine how are they related. In the second part of the paper we study slender groups in the context of co-small objects in certain categories, and give several new applications including the proof that certain homology groups of Barratt-Milnor spaces are cotorsion groups and a universal coefficients theorem for Čech cohomology with coefficients in a slender group.

show abstract

Section: Introductionmentioning

confidence: 99%

Inverse limit slender groups

Conner¹,

Herfort²,

Kent³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…They showed that many interesting groups, including free groups, free abelian groups and torsion-free word-hyperbolic groups, are lch-slender and cm-slender and that for abelian groups we recover the usual slender groups. Several types and properties of topological groups, and automatically continuous homomorphisms, have been studied in [9,24]. Most recently, Corson and Varghese [10] strengthened the connection between slender groups and automatic continuity by showing that a group is lch-slender if it is torsion-free and does not contain Q or p-adic integers for any p.…”

mentioning

confidence: 99%

Inverse limit slender groups

et al. 2023

View full text Add to dashboard Cite

Classically, an abelian group G is said to be slender if every homomorphism from the countable product Z N N to G factors through the projection to some finite product Z n . Various authors have proposed generalizations to non-commutative groups; this has resulted in a plethora of similar but not completely equivalent concepts. In the first part of this work we present a unified treatment of these concepts and examine how they are related. In the second part of the paper we study slender groups in the context of co-small objects in certain categories, and give several new applications, including the proof that certain homology groups of Barratt-Milnor spaces are cotorsion groups, and a universal coefficient theorem for Čech cohomology with coefficients in a slender group.

show abstract

Some generalizations of slender Abelian groups

Cited by 2 publications

References 1 publication

Inverse limit slender groups

Inverse limit slender groups

Inverse limit slender groups

Contact Info

Product

Resources

About