On the Outer Automorphism Groups of Finitely Generated, Residually Finite Groups
نویسنده
چکیده
Bumagin–Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial answer to this problem for recursively presentable groups.
منابع مشابه
On a question of Bumagin and Wise
Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise nonisomorphic finitely generated, non-recursively-presentable groups. These are the first examples of such residually finite groups.
متن کاملOn the residual finiteness of outer automorphisms of hyperbolic groups
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.
متن کاملNormal Automorphisms of Relatively Hyperbolic Groups
An automorphism α of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Autn(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal sub...
متن کاملJa n 20 06 On the residual finiteness of outer automorphisms of relatively hyperbolic groups
We show that every virtually torsion-free subgroup of the outer au-tomorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite. In an addendum, we also generalise the main result for relatively hyperbolic g...
متن کاملO ct 2 00 5 On the residual finiteness of outer automorphisms of relatively hyperbolic groups
We show that every virtually torsion-free subgroup of the outer au-tomorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite. We also generalise the main result for relatively hyperbolic groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016