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nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any...

an automorphism group is also called a symmetry group. A subgroup of an automorphism group is sometimes called a transformation group. Automorphism groups...

can be represented as the automorphism group of a connected graph – indeed, of a cubic graph. Constructing the automorphism group of a graph, in the form...

In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the...

In mathematics, the outer automorphism group of a group, G, is the quotient, Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is...

up to an element of S6 (an inner automorphism)) yields an outer automorphism S6 → S6. This map is an outer automorphism, since a transposition does not...

itself forms a group, the automorphism group of G . {\displaystyle G.} For all abelian groups there is at least the automorphism that replaces the group...

mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability...

theory, a class automorphism is an automorphism of a group that sends each element to within its conjugacy class. The class automorphisms form a subgroup...

^{0}({\mathfrak {g}})} is known as the outer automorphism group. It is known that the outer automorphism group for a simple Lie algebra g {\displaystyle...

subgroup. An IA automorphism is thus an automorphism that sends each coset of the commutator subgroup to itself. The IA automorphisms of a group form...

cases the surface X admits infinitely many conformal automorphisms (in fact, the conformal automorphism group is a complex Lie group of dimension three for...

quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automorphism for...

automorphism interchanging the two types of reflections (properly, a class of outer automorphisms, which are all conjugate by an inner automorphism)...

{\displaystyle \mathbb {R} ^{n}} in the usual way, one has the typical toral automorphism on the quotient. The fundamental group of an n-torus is a free abelian...

generates a subgroup of the automorphism group of S. If S = Spec k is the spectrum of a finite field, then its automorphism group is the Galois group of...

power automorphism of a group is an automorphism that takes each subgroup of the group to within itself. It is worth noting that the power automorphism of...

said to be complete if every automorphism of G is inner, and it is centerless; that is, it has a trivial outer automorphism group and trivial center. Equivalently...

exchanged by an outer automorphism. Order: 214 ⋅ 36 ⋅ 56 ⋅ 7 ⋅ 11 ⋅ 19 = 273030912000000 Schur multiplier: Trivial. Outer automorphism group: Order 2. Other...

composition is an automorphism. This involution is often called the contragredient map, and it provides an example of an outer automorphism of the general...