# Category: Group automorphisms

Automorphism group
In mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the aut
Outer automorphism 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 the subgroup consisting of inner automorphisms.
Holomorph (mathematics)
In mathematics, especially in the area of algebra known as group theory, the holomorph of a group is a group that simultaneously contains (copies of) the group and its automorphism group. The holomorp
Power automorphism
In mathematics, in the realm of group theory, a 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
Class automorphism
In mathematics, in the realm of group 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 of the a
IA automorphism
In mathematics, in the realm of group theory, an IA automorphism of a group is an automorphism that acts as identity on the abelianization. The abelianization of a group is its quotient by its commuta
Inner automorphism
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 conjugating element. They can be realized via s
Quotientable automorphism
In mathematics, in the realm of group theory, a quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automor