|
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
These function are currently only available for incidence geometries.
An automorphism αof an incidence geometry
Γ(X, ~, t, I) is an automorphism of the incidence graph of
Γsuch 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 αof an incidence geometry
Γ(X, ~, t, I) is an automorphism of the incidence graph of
Γsuch 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.
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
|
