Pro-p groups with constant generating number on open subgroups

Klopsch, Benjamin; Snopce, Ilir

doi:10.1016/j.jalgebra.2010.12.016

Cited by 11 publications

(14 citation statements)

References 11 publications

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“…Hence G is one of the groups described in Corollary 1.12. This establishes [11,Corollary 2.4]; for the induction step one proceeds in the same way as in [11].…”

Section: Hereditarily Powerful Pro-p Groupsmentioning

confidence: 65%

“…In [11] the authors of the present paper used Lie ring methods to classify all finitely generated pro-p groups with constant generating number on open subgroups; see Theorem 3.1. In Section 3 we indicate how Corollary 1.12 yields an alternative proof in the case p ≥ 3, which does not require Lie ring techniques.…”

Section: Some Applicationsmentioning

confidence: 99%

“…Conversely, Corollary 1.12 can be used to give a new proof of Theorem 3.1, at least in the case p ≥ 3. Indeed, the argument given in [11] 6, the group G is hereditarily uniform. Hence G is one of the groups described in Corollary 1.12.…”

Section: Hereditarily Powerful Pro-p Groupsmentioning

confidence: 99%

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A CHARACTERIZATION OF UNIFORM PRO-p GROUPS

Klopsch

Snopce

2014

The Quarterly Journal of Mathematics

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“…Hence G is one of the groups described in Corollary 1.12. This establishes [11,Corollary 2.4]; for the induction step one proceeds in the same way as in [11].…”

Section: Hereditarily Powerful Pro-p Groupsmentioning

confidence: 65%

Section: Some Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

A CHARACTERIZATION OF UNIFORM PRO-p GROUPS

Klopsch

Snopce

2014

The Quarterly Journal of Mathematics

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“…There has been much work related to this notion, e.g. [12] and papers verifying the Nielsen-Schreier formula for families of groups other than free groups. Our second theorem states that there is a close connection between the minimal number of generators of a Houghton group and its finite index subgroups.…”

Section: Introduction Introduced Inmentioning

confidence: 99%

On the finite index subgroups of Houghton’s groups

Cox

2022

Arch. Math.

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Houghton’s groups $$H_2, H_3, \ldots $$ H 2 , H 3 , … are certain infinite permutation groups acting on a countably infinite set; they have been studied, among other things, for their finiteness properties. In this note we describe all of the finite index subgroups of each Houghton group, and their isomorphism types. Using the standard notation that d(G) denotes the minimal size of a generating set for G, we then show, for each $$n\in \{2, 3,\ldots \}$$ n ∈ { 2 , 3 , … } and U of finite index in $$H_n$$ H n , that $$d(U)\in \{d(H_n), d(H_n)+1\}$$ d ( U ) ∈ { d ( H n ) , d ( H n ) + 1 } and characterise when each of these cases occurs.

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“…Note that hereditarily uniform pro-p groups have been classified and all those groups can be realised as maximal pro-p Galois groups (cf. [30], [44] and [17]; see also [16]).…”

Section: Theorem D a P-adic Analytic Pro-p Group G Is H • -Quadratic ...mentioning

confidence: 99%

On pro-$p$ groups with quadratic cohomology

Quadrelli¹,

Snopce²,

Vannacci³

2019

Preprint

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The main purpose of this article is to study pro-p groups with quadratic Fp-cohomology algebra, i.e. H • -quadratic pro-p groups. Prime examples of such groups are the maximal Galois pro-p groups of fields containing a primitive root of unity of order p.We show that the amalgamated free product and HNN-extension of H • -quadratic pro-p groups is H • -quadratic, under certain necessary conditions. Moreover, we introduce and investigate a new family of pro-p groups that yields many new examples of H • -quadratic groups: p-RAAGs. These examples generalise right angled Artin groups in the category of pro-p groups. Finally, we explore "Tits alternative behaviour" of H • -quadratic pro-p groups.

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Pro-p groups with constant generating number on open subgroups

Cited by 11 publications

References 11 publications

A CHARACTERIZATION OF UNIFORM PRO-p GROUPS

A CHARACTERIZATION OF UNIFORM PRO-p GROUPS

On the finite index subgroups of Houghton’s groups

On pro-$p$ groups with quadratic cohomology

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