Automorphism Group and Correlation Group

These commands are only available for incidence geometries in the present version.

An automorphism alpha of an incidence geometry Gamma(X, ~, t, I) is an automorphism of the incidence graph of Gamma such that for all x in X, t(alpha(x)) = t(x). In other words, an automorphism cannot change the type of an element. The automorphism group of Gamma, denoted Aut(Gamma), is the group of all automorphisms of Gamma.

A correlation alpha of an incidence geometry Gamma(X, ~, t, I) is an automorphism of the incidence graph of Gamma such that for all x, y in X, t(x) = t(y) Rightarrow t(alpha(x)) = t(alpha(y)). The correlation group of Gamma, denoted Cor(Gamma), is the group of all correlations of Gamma.

It is obvious that Aut(Gamma) is a subgroup of Cor(Gamma).

For an incidence geometry Gamma, we can compute Aut(Gamma) and Cor(Gamma) using the commands described below.

AutomorphismGroup(D) : IncGeom -> GrpPerm

Given an incidence geometry D, return the group of type--preserving automorphisms of D as a permutation group of type GrpPerm acting on the set of elements of D.

CorrelationGroup(D) : IncGeom -> GrpPerm

Given an incidence geometry D, return the group of automorphisms of D as a permutation group of type GrpPerm acting of the set on elements of D.