Weakly amenable groups and amalgamated products
نویسندگان
چکیده
منابع مشابه
Amenable Actions of Amalgamated Free Products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملWeakly Amenable Groups
In the present paper we construct the first examples of finitely generated non–amenable groups whose left regular representations are not uniformly isolated from the trivial representation.
متن کاملAmalgamated Products and Properly 3-realizable Groups
In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) = G and whose universal cover K̃ has the proper homotopy type of a 3-manifold (with boundary).
متن کامل2 00 9 Amenable actions of amalgamated free products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملKnapsack in Graph Groups, HNN-Extensions and Amalgamated Products
It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1993-1119263-9