On amenability of groups generated by homogeneous automorphisms and their cracks
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Adam Woryna
Abstract
We investigate the recently obtained condition [9] for amenability of groups generated by bounded automorphisms of a spherically homogeneous rooted tree together with our group construction [13] based on the notion of a homogeneous automorphism and its crack. We establish the general condition answering the question when a group generated by homogeneous automorphisms and their cracks is amenable. We apply this result to the universal construction from [13], providing finitely generated, amenable groups, which are dense in infinitely iterated, permutational wreath products of transitive, Abelian groups.
Acknowledgements
We would like to thank to the anonymous reviewer for valuable comments and for an accurate suggestion which encourage us to state and prove a more general result.
References
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
Artikel in diesem Heft
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
