6 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 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…
Groups represented by incidence geometries
Dimitri Leemans, Klara Stokes, Philippe Tranchida
The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. Mo…
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…
Geometries with trialities arising from linear spaces
Rémi Delaby, Dimitri Leemans, Philippe Tranchida
A triality is a sort of super-symmetry that exchanges the types of the elements of an incidence geometry in cycles of length three. Although geometries with trialities exhibit fasc…
Triples of involutions in PGL(2,q) and their incidence geometries
Philippe Tranchida
For with an odd prime, the projective linear group can be seen as the stabilizer of a conic in a projective plane . In that setting, invol…