Dowling group geometries and the critical problem

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...

Characterizing Combinatorial Geometries by Numerical Invariants

We show that the projective geometry PG(r − 1, q) for r > 3 is the only rank-r (combinatorial) geometry with (qr − 1)/(q − 1) points in which all lines have at least q + 1 points. For r = 3, these numerical invariants do not distinguish between projective planes of the same order, but they do distinguish projective planes from other rank-3 geometries. We give similar characterizations of affine...

Extending a matroid by a cocircuit

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and new results about line-closed geometries. We complement these topics by showing that line-closure gives simple geometric proofs of the (mostly known) basic results about Dowling lattices. We pursue the topic of line-clo...

The Effect of Problem-Based Learning Clinical Education on Nursing Student's Critical Thinking

Background: Problem-based clinical education is an effective strategy for enhancing creativity, group work, leadership and problem-solving skills in nursing students. It seems PBL can improve nursing students’ critical thinking skills. The aim of this study was to investigate the effects of problem-based clinical education on nursing students’ critical thinking. Methods: This randomized control...

Matching Theorems for Combinatorial Geometries