Definitions for Inner automorphism

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  1. Inner automorphism

    In abstract algebra an inner automorphism is a function which, informally, involves a certain operation being applied, then another operation being performed, and then the initial operation being reversed. Sometimes the initial action and its subsequent reversal change the overall result, and sometimes they do not. More formally an inner automorphism of a group G is a function: defined for all x in G by−1 where a is a given fixed element of G, and where we deem the action of group elements to occur on the right. The operation a−1xa is called conjugation. In fact−1 is equivalent to saying 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.


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