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On totally inert simple groups

Martyn Dixon, Martin Evans, Antonio Tortora (2010)

Open Mathematics

A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.

On transitivity of pronormality

Leonid A. Kurdachenko, Igor Ya. Subbotin (2002)

Commentationes Mathematicae Universitatis Carolinae

This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.

Optics in Croke-Kleiner Spaces

Fredric D. Ancel, Julia M. Wilson (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We explore the interior geometry of the CAT(0) spaces X α : 0 < α π / 2 , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....

Orderable 3-manifold groups

Steven Boyer, Dale Rolfsen, Bert Wiest (2005)

Annales de l’institut Fourier

We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P 2 -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability...

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