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Primitive elements in the free product of two finite cyclic groups

  • M. Lustig
  • E. -M. Thiele
  • H. Zieschang
Article

Abstract

For the free product 〈s |s a=1〉*〈t|t b=1〉 we give a precise description of the wordsu ins,t which are primitive (i.e. there exists an elementv such thatu,v generate the whole group).

Keywords

Free Group Number Theory Differential Geometry Cyclic Group Free Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J. Nielsen. Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden.Math. Ann. 78 (1918), 385–397.CrossRefGoogle Scholar
  2. [2]
    R.P. Osborne andH. Zieschang. Primitives in the Free Group on Two Generators.Invent. math. 63 (1981), 17–24.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    E.-M. Thiele.Primitive Elemente im freien Produkt zweier zyklischer Gruppen. Diplomarbeit, Bochum 1990.Google Scholar

Copyright information

© Mathematische Seminar 1995

Authors and Affiliations

  • M. Lustig
    • 1
  • E. -M. Thiele
    • 1
  • H. Zieschang
    • 1
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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