Editing Inner automorphism (section)

{{Short description|Automorphism of a group, ring, or algebra given by the conjugation action of one of its elements}}
In [[abstract algebra]], an '''inner automorphism''' is an [[automorphism]] of a [[Group (mathematics)|group]], [[Ring (mathematics)|ring]], or [[Algebra over a field|algebra]] given by the [[Conjugacy class#Conjugacy as group action|conjugation action]] of a fixed element, called the ''conjugating element''. They can be realized via operations from within the group itself, hence the adjective "inner". These inner automorphisms form a [[subgroup]] of the automorphism group, and the [[Quotient_group|quotient]] of the automorphism group by this subgroup is defined as the [[outer automorphism group]].