Let us recall definitions of the properties described in this section.
An incidence geometry Gamma is flag--transitive if for every two flags x, y of the same type of Gamma, there exists an element g of Aut(Gamma) such that g(x) = y. We also say that Aut(Gamma) acts flag--transitively in this case.
Moreover, it is a flag--transitive geometry if it contains at least one chamber.
A coset geometry Gamma(G; (G_i)_(i in I)) is flag--transitive if for every two flags x, y of the same type of Gamma, there exists an element g of G such that g(x) = y. It is then a flag--transitive geometry since the set { (G_i)_(i in I) } is a chamber of Gamma.
Given an incidence geometry D, return true iff the automorphism group of D acts flag--transitively on D and D has at least one chamber.
Given a coset geometry C, return true iff the group of C acts flag--transitively on C.
Given a flag--transitive incidence geometry D, return true iff every flag of D is contained in at least two chambers.
Given a flag--transitive coset geometry C, return true iff every flag of C is contained in at least two chambers.
Given a flag--transitive incidence geometry D, return true iff every flag of D is contained in exactly two chambers.
Given a flag--transitive coset geometry C, return true iff every flag of C is contained in exactly chambers.
Given a flag--transitive incidence geometry D, return true iff every flag of D is contained in exactly three chambers.
Given a flag--transitive coset geometry C, return true iff every flag of C is contained in exactly three chambers.
Given a flag--transitive incidence geometry D, return true iff every residue of rank at least two of D has a connected incidence graph.
Given a flag--transitive coset geometry C, return true iff every residue of rank at least two of C has a connected incidence graph.[Next][Prev] [Right] [Left] [Up] [Index] [Root]