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{{r|Field automorphism}}

...ernel]] of the [[group homomorphism|homomorphism]] to ''G'' to its [[inner automorphism]] group.

{{r|Field automorphism}}

{{r|Field automorphism}}

{{r|Field automorphism}}

{{r|Field automorphism}}

{{r|Field automorphism}}

{{r|Field automorphism}}

{{r|Automorphism}}

{{r|Field automorphism}}

...p]] is cyclic of order two, with the non-trivial element being the [[field automorphism]] If ''F'' is a complex quadratic field then this automorphism is induced by [[complex conjugation]].

...ath)|matrix]]'''. A Moore matrix has successive powers of the [[Frobenius automorphism]] applied to the first column, i.e., an ''m'' × ''n'' matrix

{{r|Automorphism}}

*a group containing all [[field automorphism]]s in ''L'' that leave the elements in ''K'' untouched - the Galois group o ...y 2 automorphisms of L that leave every element of Q alone: the do-nothing automorphism <math>\phi_0: a+b r_0 \rightarrow a + b r_0 </math> and the map <math>\ph

...oup is, in general, difficult. Because abelian groups have a trivial inner automorphism subgroup, finding automorphisms for abelian groups is, strangely enough, ha

...s therefore also [[surjective function|surjective]] (it is the [[Frobenius automorphism]]). Suppose that ''F'' is finite, of characteristic two. The Frobenius map is an automorphism and so its [[inverse function|inverse]], the square root map is defined eve

* The [[automorphism group]] of an algebraic structure acts on the structure.

...e sense that every point can be transformed into every other point by some automorphism.