The Figure Eight Knot Group Is Conjugacy Separable

Chagas, S. C.; Zalesskiĭ, Pavel

doi:10.1142/s0219498809003497

Cited by 6 publications

(7 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 2.7 in [6]). In this case the vertex set is V (S(  G)) =  G/  G 1 , the edge set is E(S(  G)) =  G/  H, and the initial and terminal vertices of an edge g  H are respectively g  G 1 and gt  G 1 .…”

Section: Right Angled Artin Groupsmentioning

confidence: 96%

Hereditary conjugacy separability of free products with amalgamation

Chagas

Zalesskiĭ

2013

Journal of Pure and Applied Algebra

View full text Add to dashboard Cite

Section: Right Angled Artin Groupsmentioning

confidence: 96%

Hereditary conjugacy separability of free products with amalgamation

Chagas

Zalesskiĭ

2013

Journal of Pure and Applied Algebra

View full text Add to dashboard Cite

“…clearly ∆ is finite. By the pro-p version of Lemma 2.14 in [4] for any connected component Ω of the preimage of ∆ in T and its setwise stabilizer Stab G (Ω) we have Ω/Stab G (Ω) = ∆. By Proposition 4.4 in [41] a pro-p group acting on a pro-p tree cofinitely is the fundamental group of a finite graph of groups in a standard manner, i.e., in our case Stab G (Ω) = Π 1 (G, ∆).…”

Section: Acylindrical Actionmentioning

confidence: 99%

“…Let ∆ α be a connected component of ∆. By the pro-p version of Lemma 2.14 in [4] for any connected component Ω α of the preimage of ∆ α in T and its setwise stabilizer…”

Section: Acylindrical Actionmentioning

confidence: 99%

Subgroup properties of pro- $$p$$ p extensions of centralizers

Snopce

Zalesskiĭ

2013

Sel. Math. New Ser.

View full text Add to dashboard Cite

We prove that a finitely generated pro-p group acting on a prop tree T with procyclic edge stabilizers is the fundamental pro-p group of a finite graph of pro-p groups with edge and vertex groups being stabilizers of certain vertices and edges of T respectively, in the following two situations: 1) the action is n-acylindrical, i.e., any non-identity element fixes not more than n edges; 2) the group G is generated by its vertex stabilizers. This theorem is applied to obtain several results about pro-p groups from the class L defined and studied in [16] as pro-p analogues of limit groups. We prove that every pro-p group G from the class L is the fundamental pro-p group of a finite graph of pro-p groups with infinite procyclic or trivial edge groups and finitely generated vertex groups; moreover, all non-abelian vertex groups are from the class L of lower level than G with respect to the natural hierarchy. This allows us to give an affirmative answer to questions 9.1 and 9.3 in [16]. Namely, we prove that a group G from the class L has Euler-Poincaré characteristic zero if and only if it is abelian, and if every abelian pro-p subgroup of G is procyclic and G itself is not procyclic, then def(G) ≥ 2. Moreover, we prove that G satisfies the Greenberg-Stallings property and any finitely generated non-abelian subgroup of G has finite index in its commensurator.We also show that all non-solvable Demushkin groups satisfy the Greenberg-Stallings property and each of their finitely generated non-trivial subgroups has finite index in its commensurator.

show abstract

“…By Proposition 3.1, there exists a finite index hereditarily conjugacy separable subgroup H of G such that H = F Z with F free, of finite rank. Then for every h ∈ H the centralizer C G (h) is finitely generated virtually abelian by Lemma 2.2 in [9] and therefore is hereditarily conjugacy separable. The equality Theorem 3.4 in [19]).…”

Section: Groups Commensurable With Bianchi and Limit Groupsmentioning

confidence: 99%