5 papers
Coset geometries acting on their elements: The -diagonals twisting
Claudio Alexandre Piedade, Philippe Tranchida
Let be a coset incidence system and fix a type . We use the orbits of the group of on pairs of distinct -elements to define a Coxeter graph. The action on the -ele…
The Geometry of Pattern Groups
João Dias, Claudio Alexandre Piedade
Coset incidence geometries are an important tool which connect group theory and geometry. While the representations of the unitriangular group and its pattern subgroups have been s…
The geometry of wreath and semi-direct products
Claudio Alexandre Piedade, Philippe Tranchida
Coset geometries are incidence geometries constructed from a group and a system of subgroups of subgroups of . For any algebraic group operation, it is the…
Regular polytopes of rank for transitive groups of degree
Maria Elisa Fernandes, Claudio Alexandre Piedade
Previous research established that the maximal rank of the abstract regular polytopes whose automorphism group is a transitive proper subgroup of $\mbox{S}_n$ is . Up to i…
From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries
Claudio Alexandre Piedade, Philippe Tranchida
Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon t…