Examples of 'automorphism group' in a sentence
Meaning of "automorphism group"
In mathematics, the collection of all automorphisms, which are bijective transformations, that preserve certain structure or properties of an object
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- The group of automorphisms of a given set or other mathematical object, with the group operation being function composition.
How to use "automorphism group" in a sentence
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automorphism group
The automorphism group is sometimes denoted DiffM.
The structure of the automorphism group is as follows.
The automorphism group is also called the isometry group.
The geometry of the outer automorphism group of a free group.
It is the automorphism group of the graph consisting of a path infinite to both sides.
The finite quotient group is precisely the automorphism group.
The outer automorphism group is usually denoted OutG.
The set of all autotopies of a quasigroup form a group with the automorphism group as a subgroup.
Inner automorphism group.
This allows us to better understand the structure of these factors and their automorphism group.
Order of automorphism group.
A distance-transitive graph is interesting partly because it has a large automorphism group.
On the automorphism group of a Lie group.
The compact form is simply connected and its outer automorphism group is the trivial group.
The full automorphism group of this hyperoval has order 3.
See also
This group is called the automorphism group of X.
The automorphism group can be identified with the stabilizer of 1 in the structure group.
The Schur multiplier and the outer automorphism group of the Monster are both trivial.
The set of all automorphisms of an object forms a group, called the automorphism group.
The Schur multiplier and the outer automorphism group of the Thompson group are both trivial.
In wider contexts, a symmetry group may be any kind of transformation group, or automorphism group.
In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges.
The automorphism group of a point x0 in X is just the fundamental group based at x0.
For example, the group G2 is the automorphism group of an octonion algebra over k.
Up to isomorphism, the Clebsch surface is the only cubic surface with this automorphism group.
The outer automorphism group is trivial and the Schur multiplier has order 2.
Both the Schur multiplier and the outer automorphism group have order 2.
As a Cayley graph, its automorphism group acts transitively on its vertices, making it vertex transitive.
Its Schur multiplier is trivial and its outer automorphism group has order 2.
Galois group, The automorphism group of a Galois extension.
The simply connected group has center Z and its outer automorphism group has order 2.
If the inner automorphism group of a perfect group G is simple, then G is called quasisimple.
A group of type G2 is always the automorphism group of an octonion algebra.
Its automorphism group is the exceptional Lie group F ₄.
Mitchell's group is an index 2 subgroup of the automorphism group of the Coxeter-Todd lattice.
It has an automorphism group of order 54 automorphisms.
More formally, a " representation " means a homomorphism from the group to the automorphism group of an object.
The automorphism group of the graph consisting only of a cycle with n vertices ( if n ≥ 3 ).
Thus, if " G " has trivial center it can be embedded into its own automorphism group.
Its automorphism group is isomorphic to the group of units of the ring Z, i . e.
The Schur multiplier has order 3, and its outer automorphism group has order 2.
The automorphism group of the Ljubljana graph is a group of order 168.
First we define the action of the automorphism group Aut ( Fn ) on Xn.
The automorphism group of the Coxeter graph is a group of order 336.
For n 1 and 2, the automorphism group is trivial.
The automorphism group of the Möbius - Kantor graph is a group of order 96.
Algebraic properties = = The automorphism group of the Pappus graph is a group of order 216.
The automorphism group is sometimes denoted Diff ( M ).
Algebraic properties = = The automorphism group of the Nauru graph is a group of order 144.
The automorphism group of " X " is also called the symmetric group on " X.
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Examples of using Automorphism
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The automorphism group is sometimes denoted DiffM
The structure of the automorphism group is as follows
An automorphism always maps the identity to itself
