Automorphism Groups of Higher-Weight Dowling Geometries

On Dowling geometries of infinite groups

A finite subgeometry of a Dowling geometry for an infinite group is exhibited, which cannot be embedded in a Dowling geometry for any finite group; this provides a negative answer to a question of Bonin. The question addressed herein is motivated by the following fundamental result of Rado, concerning the embeddability of finite geometries in projective geometries [Ra, Theorem 4]: Theorem. Ever...

Automorphism Groups of Parabolic Geometries

We show that elementary algebraic techniques lead to surprising results on automorphism groups of Cartan geometries and especially parabolic geometries. The example of three–dimensional CR structures is discussed in detail.

On Automorphism Groups of Parabolic Geometries

Linfan Mao Automorphism Groups of Maps, Surfaces and Smarandache Geometries

A combinatorial map is a connected topological graph cellularly embeddedin a surface. This monograph concentrates on the automorphism groupof a map, which is related to the automorphism groups of a Klein surfaceand a Smarandache manifold, also applied to the enumeration of unrootedmaps on orientable and non-orientable surfaces. A number of results for theautomorphism groups ...

An embedding theorem for automorphism groups of Cartan geometries

The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, and which cannot? Which algebraic properties of the acting group have strong implications on the geometry of the manifold, such as local homogeneity, or on the dynamics of the action? These questions ...