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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...

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...

can be represented as the automorphism group of a connected graph – indeed, of a cubic graph. Constructing the automorphism group is at least as difficult...

an automorphism of a conjugacy class is always a conjugacy class (the same or another). The composition of two automorphisms is again an automorphism, and...

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)...

important class that includes finite fields. The endomorphism maps every element to its p-th power. In certain contexts it is an automorphism, but this...

the mapping class group Mod(S). In fact, the proof of the classification theorem leads to a canonical representative of each mapping class with good geometric...

{\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...

theory, the automorphism group of a free group is a discrete group of automorphisms of a free group. The quotient by the inner automorphisms is the outer...

{\displaystyle \varphi (x)=gxg^{-1}} is an automorphism of G {\displaystyle G} called an inner automorphism. See the next property for an example. If a...

mapping class group of the pair is the isotopy-classes of automorphisms of the pair, where an automorphism of (X,A) is defined as an automorphism of X that...

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

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

conjugacy-closed normal subgroups is that all class automorphisms of the whole group restrict to class automorphisms of the subgroup. The following facts are...

In number theory, the class number formula relates many important invariants of a algebraic number field to a special value of its Dedekind zeta function...

the letters A to O. From the number of automorphisms for each solution and the definition of an automorphism group, the total number of solutions including...

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