منابع مشابه
Countable Primitive Groups
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...
متن کامل6 Countable Primitive Linear Groups
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...
متن کاملConstructing continuum many countable, primitive, unbalanced digraphs
We construct continuum many non-isomorphic countable digraphs which are highly arc-transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive. 2000 Mathematics Subject Classification: 20B07, 20B15, 03C50, 05C20.
متن کاملAutomorphism groups of countable structures
Suppose M is a countable first-order structure with a ‘rich’ automorphism group Aut(M). We will study Aut(M) both as a group and as a topological group, where the topology is that of pointwise convergence. This involves a mixture of model theory, group theory, combinatorics, descriptive set theory and topological dynamics. Here, ‘rich’ is undefined and depends on the context, but examples which...
متن کاملDistinguishing Primitive Permutation Groups
Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2007
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-007-0630-y