Definitions

1. An automorphism is a morphism that is both an endomorphism and an isomorphism.
2. An automorphism is called (non-) symplectic if the induced operation on the global nowhere vanishing holomorphic two form is (non-) trivial. (Web site)
3. An automorphism (specifically, a group automorphism) is simply an isomorphism that is from a group to itself.
4. The automorphism is furthermore determined completely by its effects on any set of generators for. (Web site)
5. Every automorphism is an isometry with respect to this metric.

Automorphism Group Computation

1. Automorphism group computation and isomorphism checking for graphs.

Tame Automorphism Group

1. One can not decide whether g is in the tame automorphism group since there is no theorem for the above factorization. (Web site)

Computing Automorphism Groups

1. Nauty - A program for computing automorphism groups of graphs and digraphs. (Web site)
2. The functions for computing automorphism groups and isometries of lattices are based on the AUTO and ISOM programs of Bernd Souvignier.

Outer Automorphism Groups

1. Sporadic simple groups and alternating groups (other than the alternating group A 6; see below) all have outer automorphism groups of order 1 or 2.

Tame Automorphisms

1. The group generated by all tame automorphisms is called the tame automorphism group. (Web site)

Tame Automorphism

1. Remark 2: In general, it is convenient to require that a tame automorphism.o slashed. (Web site)

Class Automorphism

1. Every class automorphism is a center-fixing automorphism, that is, it fixes all points in the center. (Web site)
2. Every inner automorphism is a class automorphism. (Web site)

Aut

1. For an automorphism aut, Inverse returns the inverse automorphism aut 1.
2. Every automorphism of A is a linear transformation, so Aut(A) is isomorphic to the general linear group GL n(Z p). (Web site)
3. The automorphism group of an object X in a category C is denoted Aut C(X), or simply Aut(X) if the category is clear from context.

Inner Automorphism Group

1. The image of the group under this map is termed the inner automorphism group, and automorphisms arising as such images are termed inner automorphisms. (Web site)
2. For n 3, except for n = 6, the automorphism group of A n is the symmetric group S n, with inner automorphism group A n and outer automorphism group Z 2.
3. Thus for n odd, the inner automorphism group has order 2 n, and for n even the inner automorphism group has order n. (Web site)

Full Automorphism Groups

1. Namely, the informations about duality of constructed designs and about the structures of the full automorphism groups of these designs are also given.

Full Automorphism Group

1. In this paper, it is proved that for many groups a simple lifting criterion determines whether the admitted automorphisms form the full automorphism group.
2. For example, taking only the identity gives the trivial lower bound, which is what would happen if every graph had full automorphism group. (Web site)
3. For n = 6, there is an exceptional outer automorphism of A 6, so S 6 is not the full automorphism group of A 6. (Web site)

Riemann Surfaces

1. The criterion is employed to give numerous examples of Riemann surfaces whose defining equations and full automorphism groups are determined.

Automorphism Groups

1. Groups are used throughout mathematics and the sciences, often to capture the internal symmetry of other structures, in the form of automorphism groups. (Web site)
2. K.-H. Neeb, On the classification of rational quantum tori and the structure of their automorphism groups, Canadian Math.
3. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows.

Linear

1. Using the notion of sheaves generated by global sections, it can be shown that any algebraic (not necessarily linear) automorphism has to be linear, i.e. (Web site)
2. But we can check that a transposition (i j) permutes the totals without fixed points so this automorphism is not linear. (Web site)

Equal

1. There is an abyss between our knowledge of the automorphism group of K 2 and the automorphism group of K n+r for n+r greater than or equal to 3. (Web site)

Square

1. Any automorphism of the latter arises from a similarity, and in fact from an orthogonal transformation if its determinant is a square.

Normal

1. Note that the condition for all normal subgroups N of G is not sufficient for the automorphism to be a normal automorphism. (Web site)
2. Every normal automorphism of the whole group restricts to a normal automorphism of the subgroup.

Sequence

1. Automorphism(A,F): Sch,SeqEnum - MapSch The automorphism of the affine space A determined by the sequence of functions F defined on A.
2. Automorphism(P,F): Prj, SeqEnum - MapSch The automorphism of the projective space P determined by the sequence of polynomials F defined on P.

Step

1. The next step is to apply an automorphism that makes y and z real while leaving x alone. (Web site)
2. Finally the cyphertext is decrypted with a private key in step 16, again using a tame automorphism based algorithm. (Web site)

Scheme

1. If a stack has an object with an automorphism other that the identity, then the stack cannot be represented by a scheme. (Web site)
2. The present invention relates to a tame automorphism based public key encryption system or scheme. (Web site)

Classification

1. This paper contains a classification of finite linear spaces with an automorphism group which is an almost simple group of Lie type acting flag-transitively.
2. We presented the classification of symmetric block designs of order nine admitting an automorphism of order six.
3. For automorphism groups of measure spaces this makes it possible to obtain a classification of all unitary representations. (Web site)

General

1. In certain contexts it is an automorphism, but this is not true in general.
2. In general, S is an antihomomorphism, so S 2 is a homomorphism, which is therefore an automorphism if S was invertible (as may be required).
3. At the end of the class we also mentioned the idea of automorphism in general.

Coloring

1. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. (Web site)

Representation

1. So any automorphism of the Heisenberg group acts on this representation H.
2. The boundary morphism maps s in S to the representation of the inner automorphism of S by s. (Web site)

Abstract

1. Abstract: A graph labeling is "distinguishing" if no nontrivial automorphism (i.e., symmetry) of the graph preserves it. (Web site)

Sigma

1. If is a homomorphism of groups, and σ is an inner automorphism of G, then there exists an inner automorphism σ' of H such that. (Web site)

Function

1. Which means that every inner automorphism of the whole group must restrict to a function on the subgroup. (Web site)
2. The function returns the automorphism group of G as a group of type GrpAuto.

Symmetric

1. Automorphism group For more details on this topic, see Automorphisms of the symmetric and alternating groups. (Web site)

Outer Automorphism Group

1. Max Dehn and Jakob Nielsen showed that it can be identified with the outer automorphism group of the fundamental group of the surface. (Web site)
2. The alternating groups usually have an outer automorphism group of order 2, but the alternating group on 6 points has an outer automorphism group of order 4.
3. For n = 3 the automorphism group is Z 2, with trivial inner automorphism group and outer automorphism group Z 2. (Web site)

Center

1. This corresponds to the algebraic condition that any automorphism on the fundamental group of M preserves the center of the group. (Web site)
2. The Lie algebra of the orthogonal group O 3(R). The simply connected group has center of order 2 and trivial outer automorphism group, and is a spin group. (Web site)
3. For, S n is a complete group: its center and outer automorphism group are both trivial. (Web site)

Theory

1. Here is one consequence of this theory: Let and let be the Galois automorphism where and. (Web site)

Manifold

1. Abstract. We associate a certain G-structure with a causal structure on a manifold, and show the coincidence of the automorphism groups of both structures. (Web site)
2. In order to characterize the boundedness several conditions on automorphism groups of an open manifold are introduced.

Conversely

1. Conversely, for S n has no outer automorphisms, and for it has no center, so for it is a complete group, as discussed in automorphism group, below. (Web site)

Inner Automorphisms

1. But an automorphism that stabilizes the transpositions is inner, so the inner automorphisms are an index 2 subgroup of Aut(S 6), so Out(S 6) = C 2. (Web site)
2. If G 1 and G 2 are two groups, and σ 1 and σ 2 are inner automorphisms on G 1 and on G 2 respectively, then is an inner automorphism on. (Web site)
3. One important subgroup of the automorphism group is the set of all inner automorphisms. (Web site)

Hence

1. Hence, the inner automorphisms form a subgroup of the automorphism group, termed the inner automorphism group. (Web site)

Problem

1. Problem: Prove that any automorphism of a field is the identity map on its simple subfield.
2. The graph automorphism problem is the problem of testing whether a graph has a nontrivial automorphism. (Web site)
3. It is an open problem in mathematics whether the automorphism group of K[x.sub.1,. (Web site)

Math

1. PlanetMath: automorphism (more info) Math for the people, by the people.

Action

1. Hence, the automorphism group acts on itself by conjugation, and this action can be viewed in terms of just changing the labels on the underlying set. (Web site)
2. In order to make the automorphism group G of X as large as possible, we want the area of its fundamental domain D for this action to be as small as possible. (Web site)
3. Three constructions are given: direct sum, extension, and action of the automorphism group of the code.

Elements

1. In the case of groups, the inner automorphism s are the conjugations by the elements of the group itself. (Web site)
2. Thus this automorphism generates Z 6. There is one more automorphism with this property: multiplying all elements of Z 7 by 5, modulo 7. (Web site)
3. For example to compute the size of such an automorphism group all elements are computed.

Subset

1. For n -dimensional V, the automorphism group of V is identified with a subset of complex square-matrices of order n. (Web site)
2. The automorphism group often stores a ``NiceMonomorphism'' (see NiceMonomorphism) to a permutation group, obtained by the action on a subset of obj. (Web site)

Euclidean Space

1. Euclidean space is homogeneous in the sense that every point can be transformed into every other point by some automorphism. (Web site)

Space

1. When all the vector spaces are the same, permutation of the factors doesn't change the space and so constitutes an automorphism. (Web site)
2. Gartside spoke at symposium about the action of an automorphism group on the space of substructures.

Orbits

1. Boštjan Kuzman: On tetravalent bicirculants A bicirculant is a graph that admits an automorphism with exactly two orbits of equal size.
2. ABSTRACT: An (abstract) polytope is called a two-orbit polytope if its automorphism group has exactly two orbits on the flags. (Web site)
3. The conjugacy classes of these E 0 -semigroups correspond to the orbits of the action of the automorphism group of the product system on unital vectors.

Algebraic

1. Then, for any, we have an automorphism of X (which may be a self-homeomorphism, self-diffeomorphism, or algebraic automorphism). (Web site)
2. Every (biregular) algebraic automorphism of a projective space is projective linear.
3. Since our groups are algebraic, a diagonal automorphism is just a special case of an inner automorphism.

Analogue

1. We prove an analogue of this theorem for the outer automorphism group of a free group.

Matrix

1. In other words, it creates the automorphism of P by the matrix having the coordinates of the n + 1 points of Q as its columns.
2. The matrix of any automorphism in with respect to is called a symplectic matrix.
3. Matrix(f): MapSch - Mtrx The matrix corresponding to the linear automorphism f of a projective space.

Categories

1. Group
2. Science > Mathematics > Algebra > Isomorphism
3. Graph
4. Information > Science > Mathematics > Subgroup
5. Science > Mathematics > Algebra > Homomorphism

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