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We introduce the concept of a locally finite abstract elementary class and develop the theory of excellence (with respect to disjoint ( !, k)-amalgamation) for such classes. From this we find...
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, cl...
Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their weak homotopy type ...
We show that there exists a non-linear, locally finite, simple group such that the centralizer of every non-trivial element is (locally solvable)-by-finite.
A Moufang loop is a binary system that satisfies a particular weak form of the associative law. Doro and Glauberman observed that there is a direct connection between simple Moufang loops and simple g...
The topic of the present paper is the following question. Let G be a locally finite group admitting an automorphism f of finite order such that the centralizer CG(f) satisfies certain finiteness condi...
We show that the groups mentioned in the title are solvable. Moreover, a point stabilizer H of the locally finite barely transitive group G is almost nilpotent, whenever the indices |H : H \cap Hg| (g...

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