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- Inner_automorphism abstract "In abstract algebra an inner automorphism is a functionwhich, informally, involves a certain operation being applied, then another operation (shown as x below) being performed, and then the initial operation being reversed. Sometimes the initial action and its subsequent reversal change the overall result ("raise umbrella, walk through rain, lower umbrella" has a different result from just "walk through rain"), and sometimes they do not ("take off left glove, take off right glove, put on left glove" has the same effect as "take off right glove only").More formally an inner automorphism of a group G is a function:ƒ: G → Gdefined for all x in G byƒ(x) = a−1xa,where a is a given fixed element of G, and where we deem the action of group elements to occur on the right (so this would read "a times x times a−1").The operation a−1xa is called conjugation (see also conjugacy class), and it is often of interest to distinguish the cases where conjugation by one element leaves another element unchanged (as in the "gloves" analogy above) from cases where conjugation generates a new element (as in the "umbrella" analogy). In fact, sayinga−1xa = x ("conjugation by a leaves x unchanged")is equivalent to sayingax = xa. ("a and x commute")Therefore the existence and number of inner automorphisms that are not the identity mapping is a kind of measure of the failure of the commutative law in the group.".
- Inner_automorphism wikiPageID "61839".
- Inner_automorphism wikiPageRevisionID "599137350".
- Inner_automorphism first "V.N.".
- Inner_automorphism hasPhotoCollection Inner_automorphism.
- Inner_automorphism id "I/i051230".
- Inner_automorphism last "Remeslennikov".
- Inner_automorphism title "Inner Automorphism".
- Inner_automorphism title "Inner automorphism".
- Inner_automorphism urlname "InnerAutomorphism".
- Inner_automorphism subject Category:Group_automorphisms.
- Inner_automorphism subject Category:Group_theory.
- Inner_automorphism comment "In abstract algebra an inner automorphism is a functionwhich, informally, involves a certain operation being applied, then another operation (shown as x below) being performed, and then the initial operation being reversed.".
- Inner_automorphism label "Automorfismo interno".
- Inner_automorphism label "Automorphisme intérieur".
- Inner_automorphism label "Inner automorphism".
- Inner_automorphism label "Inwendig automorfisme".
- Inner_automorphism label "內自同構".
- Inner_automorphism sameAs Automorphisme_intérieur.
- Inner_automorphism sameAs Automorfismo_interno.
- Inner_automorphism sameAs 내부자기동형사상.
- Inner_automorphism sameAs Inwendig_automorfisme.
- Inner_automorphism sameAs m.0gr2g.
- Inner_automorphism sameAs Q1139583.
- Inner_automorphism sameAs Q1139583.
- Inner_automorphism wasDerivedFrom Inner_automorphism?oldid=599137350.
- Inner_automorphism isPrimaryTopicOf Inner_automorphism.