Displaying similar documents to “Splittings of groups and intersection numbers.”

Commensurations of Out ( F n )

Benson Farb, Michael Handel (2007)

Publications Mathématiques de l'IHÉS

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Let Out(F) denote the outer automorphism group of the free group F with >3. We prove that for any finite index subgroup Γ<Out(F), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F). We prove that Γ is : every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F)) is isomorphic to Out(F).

The geometry of abstract groups and their splittings.

Charles Terence Clegg Wall (2003)

Revista Matemática Complutense

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A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PD groups. Notions of quasi-isometry,...

Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2010)

Open Mathematics

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Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.