 inner automorphism

Math.an automorphism that maps an element x into an element of the form axa^{1} where a^{1} is the inverse of a. Cf. outer automorphism.
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Universalium. 2010.
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Universalium. 2010.
Inner automorphism — In abstract algebra an inner automorphism is a function which, informally, involves a certain operation being applied, then another one (x) performed, and then the initial operation being reversed. Sometimes this has a net effect ( take off shoes … Wikipedia
inner automorphism — Math. an automorphism that maps an element x into an element of the form axa 1 where a 1 is the inverse of a. Cf. outer automorphism … Useful english dictionary
automorphism — /aw teuh mawr fiz euhm/, n. Math. an isomorphism from a given set to itself. Cf. inner automorphism, outer automorphism. [1870 75; AUTO 1 + MORPH + ISM] * * * ▪ mathematics in mathematics, a correspondence that associates to every element… … Universalium
automorphism — /aw teuh mawr fiz euhm/, n. Math. an isomorphism from a given set to itself. Cf. inner automorphism, outer automorphism. [1870 75; AUTO 1 + MORPH + ISM] … Useful english dictionary
Automorphism — In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms… … Wikipedia
Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… … Wikipedia
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. The outer automorphism group is usually … Wikipedia
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 automorphism group. Some facts: Every inner… … Wikipedia
Extensible automorphism — In mathematics, an automorphism of a structure is said to be extensible if, for any embedding of that structure inside another structure, the automorphism can be lifted to the bigger structure.In group theory, an extensible automorphism of a… … Wikipedia
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 of an infinite group may not restrict to an… … Wikipedia