p -Adic Hurwitz groups

Džambić, Amir; Jones, Gareth A.

doi:10.1016/j.jalgebra.2013.01.007

Cited by 7 publications

(2 citation statements)

References 15 publications

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“…That Problem 5.19(i) holds in the special case of free amalgamated products of finite groups is closely related to a conjecture of Džambić-Jones [DzJ13,p. 206].…”

Section: Given Two Non-elementary Hyperbolic Groupsmentioning

confidence: 82%

Finite and Infinite Quotients of Discrete and Indiscrete Groups

Caprace¹

2019

Groups St Andrews 2017 in Birmingham

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These notes are devoted to lattices in products of trees and related topics. They provide an introduction to the construction, by M. Burger and S. Mozes, of examples of such lattices that are simple as abstract groups. Two features of that construction are emphasized: the relevance of non-discrete locally compact groups, and the two-step strategy in the proof of simplicity, addressing separately, and with completely different methods, the existence of finite and infinite quotients. A brief history of the quest for finitely generated and finitely presented infinite simple groups is also sketched. A comparison with Margulis' proof of Kneser's simplicity conjecture is discussed, and the relevance of the Classification of the Finite Simple Groups is pointed out. A final chapter is devoted to finite and infinite quotients of hyperbolic groups and their relation to the asymptotic properties of the finite simple groups. Numerous open problems are discussed along the way. arXiv:1709.05949v3 [math.GR]

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“…That Problem 5.19(i) holds in the special case of free amalgamated products of finite groups is closely related to a conjecture of Džambić-Jones [DzJ13,p. 206].…”

Section: Given Two Non-elementary Hyperbolic Groupsmentioning

confidence: 82%

Finite and Infinite Quotients of Discrete and Indiscrete Groups

Caprace¹

2019

Groups St Andrews 2017 in Birmingham

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“…In light of the following conjecture of Džambić and Jones [6], the hypothesis ( †) does not seem strong. This suggests that Theorem 1.1 could be applied to show the existence of tetravalent half-arc-transitive graphs with other vertex stabilizers as well, and thus sheds light on classifying the vertex stabilizers of finite tetravalent half-arc-transitive graphs.…”

Section: Discussionmentioning

confidence: 93%

Constructing infinitely many half-arc-transitive covers of tetravalent graphs

Spiga

Xia

2019

Preprint

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We prove that, given a finite graph Σ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of Σ. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order 2 8 of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent halfarc-transitive graphs.

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Simple Group Actions on Arc-Transitive Graphs with Prescribed Transitive Local Action

Conder

2019

2017 MATRIX Annals

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p -Adic Hurwitz groups

Cited by 7 publications

References 15 publications

Finite and Infinite Quotients of Discrete and Indiscrete Groups

Finite and Infinite Quotients of Discrete and Indiscrete Groups

Constructing infinitely many half-arc-transitive covers of tetravalent graphs

Simple Group Actions on Arc-Transitive Graphs with Prescribed Transitive Local Action

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