Finite fields | Finite groups | Matroid theory

Dowling geometry

In combinatorial mathematics, a Dowling geometry, named after Thomas A. Dowling, is a matroid associated with a group. There is a Dowling geometry of each rank for each group. If the rank is at least 3, the Dowling geometry uniquely determines the group. Dowling geometries have a role in matroid theory as universal objects (Kahn and Kung, 1982); in that respect they are analogous to projective geometries, but based on groups instead of fields. A Dowling lattice is the geometric lattice of flats associated with a Dowling geometry. The lattice and the geometry are mathematically equivalent: knowing either one determines the other. Dowling lattices, and by implication Dowling geometries, were introduced by Dowling (1973a,b). A Dowling lattice or geometry of rank n of a group G is often denoted Qn(G). (Wikipedia).

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From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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Geometric lattice | Vector space | Finite field | Partially ordered set | Quasigroup | Glossary of graph theory | Aequationes Mathematicae | Group (mathematics) | Identity element | Combinatorics | Matroid | Mathematics | Gain graph | Function (mathematics) | Field (mathematics) | Cycle (graph theory) | Biased graph | Projective geometry | Multiple edges