Abstract

Theorem II.1 shows that every subgroup M of Z is either 0 or generated by its smallest element m>0; in the latter case it is generated by m or also by —m, but by no other element of M. For cyclic groups, we have:
  • Theorem VIII.1. Let G be a cyclic group of order m, generated by an element x. Let G’ be a subgroup of G; then there is a divisor d of m such that G’ is the cyclic group of order \( \frac{m}{d} \) generated by x d .

Keywords

Fermat 

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • André Weil
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

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