Compactness of the Automorphism Group of a Topological Parallelism on Real Projective 3-Space
Dieter Betten,Rainer Löwen +1 more
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In this paper, it was shown that the identity component of the automorphism group of a topological parallelism on real projective 3-space is compact, and that at least one component of this group is, indeed, compact.Abstract:
We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.read more
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Pencilled regular parallelisms
Hans Havlicek,Rolf Riesinger +1 more
TL;DR: In this article, the existence of pencilled line sets with respect to the Klein quadric was shown to be an algebraic condition for hyperflock determining line sets (hfd line sets).
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A characterization of Clifford parallelism by automorphisms
TL;DR: Betten and Riesinger as discussed by the authors showed that Clifford parallelism admits a group of dimension at least 3, so 3 is the critical dimension for a Clifford topological parallelism.
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A characterization of Clifford parallelism by automorphisms
TL;DR: In this article, it was shown that Clifford parallelism is the only topological parallelism that admits a group of dimension at least 3, and that 3 is the critical dimension.
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Characterising Clifford parallelisms among Clifford-like parallelisms
TL;DR: In this article, the authors studied the action of the full automorphism group of a Clifford-like parallelism on parallel classes in a 3D projective double space and proved that the linear part of the group of the Clifford parallelism is the same for all Cliffordlike parallelisms which can be associated to it.
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Automorphisms of a Clifford-like parallelism
TL;DR: In this article, the automorphism group of a Clifford-like parallelism over a quaternion skew field was studied, and it was shown that over certain skew fields, it is possible to choose a group of automorphisms in such a way that the group is either properly contained in the left parallelism or coincides with the right parallelism.
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On Some Types of Topological Groups
TL;DR: In this paper, it was shown that a locally compact group G can be approximated by Lie groups, if G contains a system of normal subgroups {Na} such that G/Na are Lie groups and that the intersection of all Na coincides with the identity e.g.
BookDOI
Compact Projective Planes: With an Introduction to Octonion Geometry
TL;DR: The Mathematical Expositions series as discussed by the authors is a collection of abstractions of pure and applied mathematics, focusing on methods and ideas essential to the topics in question, as well as their relationships to other parts of mathematics.