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Russian Journal of Mathematical Physics

, Volume 26, Issue 1, pp 122–129 | Cite as

Reidemeister Classes in Some Weakly Branch Groups

  • E. V. TroitskyEmail author
Article
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Abstract

We prove that a saturated weakly branch group G on an infinite spherically symmetric rooted tree T (i.e., a group which acts on T faithfully, level-transitively, with nontrivial rigid stabilizers of all vertices, and with a transitive action on sub-trees of some characteristic subgroups of all level stabilizers) has the property R (any automorphism ϕ: GG has infinite Reidemeister number) in each of the following cases: (1) any element of Out(G) is of finite order; (2) for any ϕ, the number of orbits on levels of the tree automorphism t, such that ϕ(g) = tgt−1, is uniformly bounded and G is weakly stabilizer transitive, i.e., the intersection of stabilizers of all vertices of any level, except for successors of one vertex of the previous level, acts transitively on these successors; (3) G is finitely generated, has prime branching numbers, and is weakly stabilizer transitive with some non-Abelian quotients of stabilizers (with no restrictions on automorphisms). Some related facts and generalizations are proved.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Dept. of Mech. and Math.Moscow State UniversityGSP-1 MoscowRussia

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