Solvable subgroups of \(\text{Out}(F_n)\) are virtually Abelian.
From MaRDI portal
Publication:1826904
DOI10.1023/B:GEOM.0000022864.30278.34zbMath1052.20027arXivmath/9712219OpenAlexW2963131344MaRDI QIDQ1826904
Mladen Bestvina, Michael Handel, Mark E. Feighn
Publication date: 6 August 2004
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9712219
subgroups of finite indexouter automorphism groupsfree groupssolvable subgroupsTits alternativerelative train tracks
Subgroup theorems; subgroup growth (20E07) Geometric group theory (20F65) Topological methods in group theory (57M07) Automorphisms of infinite groups (20E36) Automorphism groups of groups (20F28) Free nonabelian groups (20E05)
Related Items
Mapping class groups and outer automorphism groups of free groups are \(C^{*}\)-simple, Separable subgroups of mapping class groups, Translation lengths of outer automorphisms of finitely generated free-by-finite groups, Free representations of outer automorphism groups of free products via characteristic abelian coverings, North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents, Subgroup Decomposition in ๐ฎ๐๐(๐ฅ_{๐}), Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of ๐ฎ๐๐(๐ฅ_{๐}), The recognition theorem for \(\text{Out}(F_n)\)., Virtually abelian subgroups of \(\mathrm{IA}_n(\mathbb{Z}/3)\) are abelian, Orbit decidability and the conjugacy problem for some extensions of groups, Vastness properties of automorphism groups of RAAGs, Commensurations of \(\text{Out}(F_n)\)., Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy, Most automorphisms of a hyperbolic group have very simple dynamics, Abelian subgroups of \(\text{Out}(F_n)\)., Axes in outer space, Actions of higher-rank lattices on free groups, Stable representatives for symmetric automorphisms of groups and the general form of the Scott conjecture, The free splitting complex of a free group, II: Loxodromic outer automorphisms