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math.GR2026
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…
math.GR2026
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…
math.GR2025
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…