What does Inner automorphism mean?
Definitions for Inner automorphism
in·ner au·to·mor·phism
This dictionary definitions page includes all the possible meanings, example usage and translations of the word Inner automorphism.
Wikipedia
Inner automorphism
In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the conjugating element. They can be realized via simple operations from within the group itself, hence the adjective "inner". These inner automorphisms form a subgroup of the automorphism group, and the quotient of the automorphism group by this subgroup is defined as the outer automorphism group.
Wikidata
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.
Numerology
Chaldean Numerology
The numerical value of Inner automorphism in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of Inner automorphism in Pythagorean Numerology is: 3
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"Inner automorphism." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/Inner+automorphism>.
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