Concept

Automorphism

Summary
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 of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object. Definition In the context of abstract algebra, a mathematical object is an algebraic structure such as a group, ring, or vector space. An automorphism is simply a bijective homomorphism of an object with itself. (The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator.) The identity morphism (identity mapping) is called the trivial automorphism in some contexts. Respectively, other (non-identity) automorphisms are called nontrivial automorphisms. The exact definition of an automorphism depends on the type of "mathemati
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications (12)

Loading

Loading

Loading

Show more
Related people (1)
Related units

No results

Related concepts (99)
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus
Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped wit
Show more
Related courses (3)
MATH-211: Group Theory
Après une introduction à la théorie des catégories, nous appliquerons la théorie générale au cas particulier des groupes, ce qui nous permettra de bien mettre en perspective des notions telles que quotients de groupe et actions de groupe.
MATH-110(a): Advanced linear algebra I
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet.
MATH-251(d): Numerical analysis
This course offers an introduction to numerical methods for the solution of mathematical problems as: solution of systems of linear and non-linear equations, functions approximation, integration and differentiation and solution of differential equations.