A Relation in Free Products

  • M. J. Wicks
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 372)


A comparative study which contrasts the theory of free groups with the theory of free products has some general interest. One area where comparison can sometimes be made in an elementary way concerns relations, and their consequences: for example, the consequences of the relation XY = YX . It has been known for some years that, in a free group, this relation is a consequence of the relation of X 2 Y 2 Z 2 = 1 [1]. We now consider the analogous situation for free products.




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  1. [1]
    R.C. Lyndon, “The equation a2b2 = c2 in free groups”, Michigan Math. J. 6 (1959), 89–95.MathSciNetMATHGoogle Scholar
  2. [2]
    M.J. Wicks, “The equation X2Y2 = e over free products”, Proc. Second Congress Singapore Nat. Acad. Science (Singapore, 1971), to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • M. J. Wicks
    • 1
  1. 1.University of SingaporeSingapore 10

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