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The Algebra of the eth Power Residues


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1 Andhra University, Waltair, India
     

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The main object of the present paper is to show that the algebra of the Gaussian periods is identical with the algebra of the eth power residues mod p where p is a prime and e is a divisor of p-1. This algebra is obviously a particular case of the algebra of the eth power residues mod N where N is any integer. Since the system of residue classes mod N is abstractly identical with a cyclic group of order N, the above algebra may be interpreted to be the algebra of the eth power residues connected with a cyclic group of order N. It is therefore natural to enquire whether there is a similar algebra connected with any finite Abelian group. We shall however show by means of an example that this is not the case.
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  • The Algebra of the eth Power Residues

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Authors

T. Venkatarayudu
Andhra University, Waltair, India

Abstract


The main object of the present paper is to show that the algebra of the Gaussian periods is identical with the algebra of the eth power residues mod p where p is a prime and e is a divisor of p-1. This algebra is obviously a particular case of the algebra of the eth power residues mod N where N is any integer. Since the system of residue classes mod N is abstractly identical with a cyclic group of order N, the above algebra may be interpreted to be the algebra of the eth power residues connected with a cyclic group of order N. It is therefore natural to enquire whether there is a similar algebra connected with any finite Abelian group. We shall however show by means of an example that this is not the case.