Automatic continuity of ℵ1-free groups

Corson, Samuel M.

doi:10.1007/s11856-020-2006-z

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…A nice subgroup characterization for n-slender cm-slender groups is still apparently beyond reach. Thus far a classification exists for such groups only in the abelian case [3].…”

Section: Proof Of Theoremmentioning

confidence: 99%

A Nunke type classification in the locally compact setting

Corson¹,

Varghese²

2019

Preprint

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“…A nice subgroup characterization for n-slender cm-slender groups is still apparently beyond reach. Thus far a classification exists for such groups only in the abelian case [3].…”

Section: Proof Of Theoremmentioning

confidence: 99%

A Nunke type classification in the locally compact setting

Corson¹,

Varghese²

2019

Preprint

Self Cite

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“…A remarkable result obtained by Dudley in [Dud61] says that any group homomorphism from a locally compact group into a free (abelian) group is continuous. Further results in this direction can be found in [BC20], [CC19], [Cor20] and in [CK20]. A characterization in terms of forbidden subgroups of G was obtained in [CV20]: Hom(LCG, G) = cHom(LCG, G) if and only if G is torsion-free and does not contain Q or the p-adic integers Z p for any prime p as a subgroup.…”

Section: Introductionmentioning

confidence: 99%

Automatic continuity for groups whose torsion subgroups are small

Keppeler¹,

Möller²,

Varghese³

2021

Preprint

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We prove that a group homomorphism ϕ : L → G from a locally compact Hausdorff group L into a discrete group G either is continuous, or there exists a normal open subgroup N ⊆ L such that ϕ(N ) is a torsion group provided that G does not include Q or the p-adic integers Z p or the Prüfer p-group Z(p ∞ ) for any prime p as a subgroup, and if the torsion subgroups of G are small in the sense that any torsion subgroup of G is artinian. In particular, if ϕ is surjective and G additionaly does not have non-trivial normal torsion subgroups, then ϕ is continuous.As an application we obtain results concerning the continuity of group homomorphisms from locally compact Hausdorff groups to many groups from geometric group theory, in particular to automorphism groups of right-angled Artin groups and to Helly groups.

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On parabolic subgroups of Artin groups

Möller,

Paris,

Varghese

2023

Isr. J. Math.

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Given an Artin group AΓ, a common strategy in the study of AΓ is the reduction to parabolic subgroups whose defining graphs have small diameter, i.e., showing that AΓ has a specific property if and only if all “small” parabolic subgroups of AΓ have this property. Since “small” parabolic subgroups are the building blocks of AΓ one needs to study their behavior, in particular their intersections. The conjecture we address here says that the class of parabolic subgroups of AΓ is closed under intersection. Under the assumption that intersections of parabolic subgroups in complete Artin groups are parabolic, we show that the intersection of a complete parabolic subgroup with an arbitrary parabolic subgroup is parabolic. Further, we connect the intersection behavior of complete parabolic subgroups of AΓ to fixed point properties and to automatic continuity of AΓ using Bass–Serre theory and a generalization of the Deligne complex.

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Automatic continuity of ℵ1-free groups

Cited by 6 publications

References 15 publications

A Nunke type classification in the locally compact setting

A Nunke type classification in the locally compact setting

Automatic continuity for groups whose torsion subgroups are small

On parabolic subgroups of Artin groups

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