These function are currently only available for incidence geometries.
An automorphism α of an incidence geometry Γ(X, ~, t, I) is an automorphism of the incidence graph of Γ such that for all x∈X, t(α(x)) = t(x). In other words, an automorphism cannot change the type of an element. The automorphism group of Γ, denoted Aut(Γ), is the group of all automorphisms of Γ.
A correlation α of an incidence geometry Γ(X, ~, t, I) is an automorphism of the incidence graph of Γ such that for all x, y∈X, t(x) = t(y) => t(α(x)) = t(α(y)). The correlation group of Γ, denoted Cor(Γ), is the group of all correlations of Γ.
It is obvious that Aut(Γ) is a subgroup of Cor(Γ).
For an incidence geometry Γ, we can compute Aut(Γ) and Cor(Γ) using the commands described below.
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.
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.