Reidemeister classes in some weakly branch groups

Abstract

We prove that a saturated weakly branch group $G$ has the property $R_{\infty }$ (any automorphism $\varphi :G\to G$ has infinite Reidemeister number) in each of the following cases: 1) any element of $Out(G)$ has finite order; 2) for any $\varphi$ the number of orbits on levels of the tree automorphism $t$ inducing $\varphi$ is uniformly bounded and $G$ is weakly stabilizer transitive; 3) $G$ is finitely generated, prime-branching, and weakly stabilizer transitive with some non-abelian stabilizers (with no restrictions on automorphisms). Some related facts and generalizations are proved.

9 pages

References in corpus (1)

• Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups

Cited by in corpus (1)

• Property $R_{\infty }$ for some spherical and affine Artin-Tits groups