Automorphism Group, Normal Extension
:Field
, bijection
is denominated an automorphism mapping.The set of automorphism mappings of
is expressed as 
.If
, then the composite mapping 
and the inverse mapping 
are also automorphism mappings, and therefore 
is also a group based on the composite mapping operation.The set
formed by 
satisfying 
for all elements 
of a subset 
of 
is a subfield of 
and is called a fixed field of 
, and 
is called a normal extension of 
.
: automorphism group of
, order 
: fixed field of In this case,
is separative on 
.If
is an irreducible polynomial having roots inside 
, 
can be decomposed into first-order factors in 
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