A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

Wilkes, Gareth

doi:10.1515/jgth-2018-0205

Cited by 3 publications

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“…For a graph of finite p-groups G = (X, G • ), properness is equivalent both to the existence of a finite quotient of Π 1 (G) into which all G x inject and to the property that the discrete fundamental group π 1 (G) (that is, the fundamental group when considered as a graph of discrete groups) is residually p. There are classical criteria for this property in the case of one-edge graphs of groups [Hig64,Cha94]. Criteria for more general graphs of groups also exist [AF13,Wil18].…”

Section: Properness Of Graphs Of Pro-p Groupsmentioning

confidence: 99%

On accessibility for pro-p groups

Wilkes

2019

Journal of Algebra

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Section: Properness Of Graphs Of Pro-p Groupsmentioning

confidence: 99%

On accessibility for pro-p groups

Wilkes

2019

Journal of Algebra

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“…It has played an influential role in recent developments related to 3manifold groups, see [AFW15]. Fairly definitive results have been established characterising the residual p-finitess of graphs of groups (see [Wil19]), drawing inspiration from Higman's foundational paper on amalgams of p-groups [Hig64].…”

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Indicability, residual finiteness, and simple subquotients of groups acting on trees

Caprace

Wesolek

2018

Geom. Topol.

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We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tree with nilpotent local action and no global fixed point is virtually indicable; that is to say, it has a finite index subgroup which surjects onto Z. The second ensures that irreducible cocompact lattices in a product of non-discrete locally compact groups such that one of the factors acts vertex-transitively on a tree with a nilpotent local action cannot be residually finite. This is derived from a general result, of independent interest, on irreducible lattices in product groups. The third implies that every non-discrete Burger-Mozes universal group of automorphisms of a tree with an arbitrary prescribed local action admits a compactly generated closed subgroup with a non-discrete simple quotient. As applications, we answer a question of D. Wise by proving the non-residual finiteness of a certain lattice in a product of two regular trees, and we obtain a negative answer to a question of C. Reid, concerning the structure theory of locally compact groups. arXiv:1708.04590v1 [math.GR]

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