Abelian Groups

  • Hans Kurzweil
  • Bernd Stellmacher
Part of the Universitext book series (UTX)


In this chapter we determine the structure of the finite Abelian groups. As a starting point we use the structure of the cyclic groups described in Section 1.4. It will turn out that every finite Abelian group is the direct product of cyclic groups. In the second section of this chapter we will show that the automorphism groups of cyclic groups are examples of Abelian groups.


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Copyright information

© Springer-Verlag New York, Inc. 2004

Authors and Affiliations

  • Hans Kurzweil
    • 1
  • Bernd Stellmacher
    • 2
  1. 1.Institute of MathematicsUniversity of Erlangen-NuremburgErlangenGermany
  2. 2.Mathematiches Seminar KielChristian-Albrechts-UniversitätKielGermany

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