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...

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...

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...

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...

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...

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

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...

^{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...