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Covers of Algebraic Curves

  • Jean Fresnel
  • Marius van der Put
Chapter
  • 992 Downloads
Part of the Progress in Mathematics book series (PM, volume 218)

Abstract

Let p be a prime number and let G be a finite group. The subgroup p(G) ⊂ G is defined as the group generated by all elements in G having as order a power of p. Equivalent definitions of p(G) are:
  1. (i)

    p(G) is the smallest normal subgroup such that the factor group G/p(G) has no elements with order p.

     
  2. ii

    p(G) is generated by all the p-Sylow subgroups of G.

     

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Jean Fresnel
    • 1
  • Marius van der Put
    • 2
  1. 1.Théorie des nombres et Algorithmique arithmétique (A2X) UMR 5465Université Bordeaux 1TalenceFrance
  2. 2.Department of MathematicsUniversity of GroningenGroningenThe Netherlands

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