Zolotarev's Lemma
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Zolotarev''s lemma in number theory states that the Legendre symbolfor an integer a modulo a prime number p, can be computed aswhere denotes the signature of a permutation and a the permutation of the residue classes mod p induced by modular multiplication by a, provided p does not divide a.In general, for any finite group G of order n, it is easy to determine the signature of the permutation g made by left-multiplication by the element g of G. The…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Zolotarev''s lemma in number theory states that the Legendre symbolfor an integer a modulo a prime number p, can be computed aswhere denotes the signature of a permutation and a the permutation of the residue classes mod p induced by modular multiplication by a, provided p does not divide a.In general, for any finite group G of order n, it is easy to determine the signature of the permutation g made by left-multiplication by the element g of G. The permutation g will be even, unless there are an odd number of orbits of even size. Assuming n even, therefore, the condition for g to be an odd permutation, when g has order k, is that n/k should be odd, or that the subgroup generated by g should have odd index.