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تسجيل مستخدم جديدNot all finitely generated groups have universal acylindrical actions
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Carolyn R. Abbott
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The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups and $operatorname{Out}(mathbb F_n)$ for $ngeq 2$. In such a group, a generalized loxodromic element is one that is loxodromic for some acylindrical action of the group on a hyperbolic space. Osin asks whether every finitely generated group has an acylindrical action on a hyperbolic space for which all generalized loxodromic elements are loxodromic. We answer this question in the negative, using Dunwoodys example of an inaccessible group as a counterexample.
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