Multiplicative Homomorphic Mapping



Suppose I have a multiplicative subgroup S_1 in the extension field K/F
generated by a q-th root of unity in K/F. I also have a multiplicative
subgroup S_2 of order q in some other finite field F'. I want to find an
invertible
group homomorphism between S_1 and S_2. Is there a way to implement
this map?


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Relevant Pages

  • Re: Field Norm
    ... >> subgroup in F_k of the same order. ... Sorry for the mistake, k-1. ... > have the multiplicative characters, ...
    (sci.math)
  • Re: Field Norm
    ... >In finite field, a norm maps element of the extension field L/F ... what is the order of the corresponding subgroup in F ...
    (sci.math)
  • Re: Group Homomorphism
    ... >>subgroup is unknown assuming we don't know the factors of n. ... >>of Z_n and there exist an inverse mapping from the range of f? ... if the multiplicative subgroup of Z_n is not ... > a finite field. ...
    (sci.math)
  • Re: Field Norm
    ... >>In finite field, a norm maps element of the extension field L/F ... what is the order of the corresponding subgroup in F ... subgroups - see what happens to their images under the norm map. ...
    (sci.math)
  • Re: Finite index subgroup
    ... If the first statement in quotation marks is true, ... Let f:G->K be a group homomorphism, and let H be a finite index ... subgroup of K. Let M = f^. ...
    (sci.math)

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