Locally compact convergence groups and $$n$$ n -transitive actions

Carette, Mathieu; Dreesen, Dennis

doi:10.1007/s00209-014-1334-2

Cited by 8 publications

(8 citation statements)

References 27 publications

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“…Some of the groups that arise have been classified directly by Radu ([16]). Boundary-2-transitive actions on locally finite trees also play prominent roles in [5] and [9].…”

Section: Example: Groups Of Tree Automorphisms Fixing One Endmentioning

confidence: 99%

Decomposition of locally compact coset spaces

Reid¹

2021

Preprint

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In [19] it was shown that a compactly generated locally compact group G admits a finite normal series (G i ) in which the factors are compact, discrete or irreducible in the sense that no closed normal subgroup of G lies properly between G i−1 and G i . In the present article, we generalize this series to an analogous decomposition of the coset space G/H with respect to closed subgroups, where G is locally compact and H is compactly generated. This time, the irreducible factors are coset spaces G i /G i−1 where G i is compactly generated and there is no closed subgroup properly between G i−1 and G i . Such irreducible coset spaces can be thought of as a generalization of primitive actions of compactly generated locally compact groups; we establish some basic properties and discuss some sources of examples.

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“…Some of the groups that arise have been classified directly by Radu ([16]). Boundary-2-transitive actions on locally finite trees also play prominent roles in [5] and [9].…”

Section: Example: Groups Of Tree Automorphisms Fixing One Endmentioning

confidence: 99%

Decomposition of locally compact coset spaces

Reid¹

2021

Preprint

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“…Remark 3.4. -Weaker characterizations of virtually free groups carry over to the class T [5]. Indeed a l.c.…”

Section: Quasi-isometric Rigidity Of Treesmentioning

confidence: 99%

Commability of groups quasi-isometric to trees

Carette¹

2018

Ann. inst. Fourier

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“…Remark 3.4. Weaker characterizations of virtually free groups carry over to the class T [CD14]. Indeed a l.c.…”

Section: 2mentioning

confidence: 99%

Commability of groups quasi-isometric to trees

Carette¹

2013

Preprint

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Commability is the finest equivalence relation between locally compact groups such that G and H are equivalent whenever there is a continuous proper homomorphism G → H with cocompact image. Answering a question of Cornulier, we show that all non-elementary locally compact groups acting geometrically on locally finite simplicial trees are commable, thereby strengthening previous forms of quasi-isometric rigidity for trees. We further show that 6 homomorphisms always suffice, and provide the first example of a pair of locally compact groups which are commable but without commation consisting of less than 6 homomorphisms. Our strong quasi-isometric rigidity also applies to products of symmetric spaces and Euclidean buildings, possibly with some factors being trees.

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Locally compact convergence groups and $$n$$ n -transitive actions

Cited by 8 publications

References 27 publications

Decomposition of locally compact coset spaces

Decomposition of locally compact coset spaces

Commability of groups quasi-isometric to trees

Commability of groups quasi-isometric to trees

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