Decision problems, complexity, traces, and representations

Lawton, Sean; Louder, Larsen; McReynolds, D. B.

doi:10.4171/ggd/393

Cited by 17 publications

(24 citation statements)

References 66 publications

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“…There are only a few results concerning the asymptotic behaviour of conjugacy separability for different classes of groups. Lawton, Louder, and McReynolds [19] demonstrate that if G is a nonabelian free group or the fundamental group of a closed oriented surface of genus g ≥ 2, then Conj G (n) n n 2 . For the class of finitely generated nilpotent groups, the second named author and Dére [7] demonstrate the following alternative.…”

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confidence: 99%

On conjugacy separability of graph products of groups

Ferov

2016

Journal of Algebra

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We show that the class of $\mathcal{C}$-hereditarily conjugacy separable groups is closed under taking arbitrary graph products whenever the class $\mathcal{C}$ is an extension closed variety of finite groups. As a consequence we show that the class of $\mathcal{C}$-conjugacy separable groups is closed under taking arbitrary graph products. In particular, we show that right angled Coxeter groups are hereditarily conjugacy separable and 2-hereditarily conjugacy separable, and we show that infinitely generated right angled Artin groups are hereditarily conjugacy separable and $p$-hereditarily conjugacy separable for every prime number $p$.Comment: 40 page

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confidence: 99%

On conjugacy separability of graph products of groups

Ferov

2016

Journal of Algebra

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“…The proof is similar to [5,Lem 1.1] (see also [6,Lem 1.2] and [30,Lem 2.1]). We first give some lemmas about the function F G,X,S before coming to our main result.…”

Section: Separability Of Extensions Of Twisted Conjugacy Separable Groupssmentioning

confidence: 58%

“…Observe that if ϕ = id, then Conj ϕ G,S is equal to the conjugacy separability Conj G,S introduced by Lawton, Louder, and McReynolds [30]; subsequently, Conj G,S (n) Tconj G,S (n). If, for some ϕ ∈ Aut(G), we have that Conj ϕ G,S (n) < ∞ for all n ∈ N, then G is ϕ-twisted conjugacy separable.…”

Section: Finitely Generated Groups and Separabilitymentioning

confidence: 99%

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Effective twisted conjugacy separability of nilpotent groups

Deré

Pengitore

2018

Math. Z.

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This paper initiates the study of effective twisted conjugacy separability for finitely generated groups, which measures the complexity of separating distinct twisted conjugacy classes via finite quotients. The focus is on nilpotent groups, and our main result shows that there is a polynomial upper bound for twisted conjugacy separability. That allows us to study regular conjugacy separability in the case of virtually nilpotent groups, where we compute a polynomial upper bound as well. As another application, we improve the work of the second author by giving a possibly sharp upper bound for the conjugacy separability for finitely generated nilpotent groups of nilpotency class 2.

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“…Recently, several effective separability results have been established; see [2][3][4][5][6]8,9,[12][13][14][15][20][21][22][23]26]. Most relevant here are the papers [9,20] where bounds on the index of the separating subgroups for free and surface groups given.…”

Section: Introductionmentioning

confidence: 99%

Zariski closures and subgroup separability

Louder

McReynolds

Patel

2017

Sel. Math. New Ser.

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The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group. Mathematics Subject Classification 20E05 · 20E26

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Decision problems, complexity, traces, and representations

Cited by 17 publications

References 66 publications

On conjugacy separability of graph products of groups

On conjugacy separability of graph products of groups

Effective twisted conjugacy separability of nilpotent groups

Zariski closures and subgroup separability

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