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

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...

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...

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...

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...

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

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...

{\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...

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...

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...

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

^{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...

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...

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

In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the...

isomorphism from a partially ordered set to itself is called an order automorphism. When an additional algebraic structure is imposed on the posets ( S...

In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient...

the automorphism group of An is the symmetric group Sn, with inner automorphism group An and outer automorphism group Z2; the outer automorphism comes...

Iskovskikh–Manin (1971) showed that the birational automorphism group of a smooth quartic 3-fold is equal to its automorphism group, which is finite. In this sense...

In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping...

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

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...

{\displaystyle E/F} and read "E over F"). An automorphism of E / F {\displaystyle E/F} is defined to be an automorphism of E {\displaystyle E} that fixes F {\displaystyle...

In mathematics, a Sastry automorphism, is an automorphism of a field of characteristic 2 satisfying some rather complicated conditions related to the problem...

D4, there is a single non-trivial automorphism (Out = C2, the cyclic group of order 2), while for D4, the automorphism group is the symmetric group on three...

of X is called an automorphism. The set of all automorphisms is a subset of End(X) with a group structure, called the automorphism group of X and denoted...

as successive transitive extensions of permutation groups, as well as automorphism groups of Steiner systems. After the Mathieu groups, no new sporadic...