Structure computation and discrete logarithms in finite abelian p-groups

  title={Structure computation and discrete logarithms in finite abelian p-groups},
  author={Andrew V. Sutherland},
  journal={Math. Comput.},
We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig—Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for H without using a relation matrix. The problem of computing a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian group G is addressed, yielding a Monte Carlo algorithm to compute the structure of G using O(|G| 1/2 ) group operations… 

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