Relation To The Transfer in Group Theory
Let G be the multiplicative group of nonzero residue classes in Z/pZ, and let H be the subgroup {+1, −1}. Consider the following coset representatives of H in G,
Applying the machinery of the transfer to this collection of coset representatives, we obtain the transfer homomorphism
which turns out to be the map that sends a to (−1)n, where a and n are as in the statement of the lemma. Gauss's lemma may then be viewed as a computation that explicitly identifies this homomorphism as being the quadratic residue character.
Read more about this topic: Gauss's Lemma (number Theory)
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