✳flâneur — a map of the web's best reading

Inner automorphism - Groupprops

groupprops.subwiki.org · 2,108 words · saved by 1 readers

An automorphism of a group is termed an inner automorphism if it can be expressed as conjugation by an element of the group. Note that the choice of conjugating element is not unique, in fact the possibilities for the conjugating element form a coset of the center. An automorphism of a group is termed an inner automorphism if there is an element in such that for all , . Note that the choice of such that need not be unique. In fact, the possibilities for , for any , form a coset of the center of . If the convention we choose is of left actions, then the inner automorphism is denoted as , and is termed the inner automorphism induced by (or conjugation by ). It is also sometimes denoted as . If the convention is to make the group act on the right, the inner automorphism induced by is defined as , and is denoted as . Note that conjugation by in one convention equals conjugation by in the other convention. The notion of inner automorphism makes good sense because of the following

Inner automorphism - Groupprops Jump to content Want site search autocompletion? See here Encountering 429 Too Many Requests errors when browsing the site? See here From Groupprops This article is about a basic definition in group theory. The article text may, however, contain advanced material. VIEW : Definitions built on this | Facts about this: ( facts closely related to Inner automorphism , all facts related to Inner automorphism ) | Survey articles about this | Survey articles about definitions built on this VIEW RELATED : Analogues of this | Variations of this | Opposites of this | [SHOW

Explore this link on the map →

related reading