Automorphism - Wikipedia
网页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.
自同构 - 百度百科
网页在数学中，自同构（automorphism）是一个数学对象对其本身的一个同构。 从某种意义上讲，是对对象本身的一种对称镜像，一种把对象映射到自身的同时保持其全部结构的一种方式。
自同构 - 维基百科，自由的百科全书
网页在圖論中，一個圖的 圖自同構 （ 英语 ： Graph automorphism ） ，是頂點的一個置換，使得邊與非邊保持不變：兩個頂點若有邊連接，則在置換下這兩頂點的像有邊連接，反之亦然。
自同构 - 维基百科，自由的百科全书
网页2024年6月30日 · 数学上，自同构（automorphism）是从一个数学对象到自身的同构，可以看为这对象的一个对称，将这对象映射到自身而保持其全部结构的一个途径。 一个对象的所有自同构的集合是一个 群 ，称为 自同构群 ，大致而言，是这对象的 对称群 。
Automorphism -- from Wolfram MathWorld
网页2024年8月22日 · An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and muomicronrhophiomegasigmaiotasigma (morphosis) "to form" or "to shape."
网页An automorphism is determined by where it sends the generators. An automorphism ˚must send generators to generators. In particular, if G is cyclic, then it determines apermutationof the set of (all possible) generators. Examples 1.There are two automorphisms of Z: the identity, and the mapping n 7!n. Thus, Aut(Z) ˘=C 2. 2.There is …
What is an automorphism group? - Mathematics Stack Exchange
网页An automorphism of a group $G$ is a group isomorphism from $G$ onto $G$. The set of automorphisms on a group forms a group itself, where the product is composition of homomorphisms. Now everywhere that I boldfaced "group", you can replace it with "ring" or "module" or "field" or "field extension".
Automorphism | Group Theory, Symmetry, Isomorphism | Britannica
网页automorphism, in mathematics, a correspondence that associates to every element in a set a unique element of the set (perhaps itself) and for which there is a companion correspondence, known as its inverse, such that one followed by the other produces the identity correspondence (i); i.e., the correspondence that associates every element with ...
网页Introductory lectures on automorphic forms. Lectures for the European School of Group Theory July, 2001, Luminy, France by Nolan R. Wallach. 1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic ...
Group Automorphism -- from Wolfram MathWorld
网页2024年8月22日 · A group automorphism is an isomorphism from a group to itself. If G is a finite multiplicative group, an automorphism of G can be described as a way of rewriting its multiplication table without altering its pattern of repeated elements.
跳至内容