Solution of the Conjugacy Problem and Malnormality of Subgroups in Certain Relative Small Cancellation Group Presentations

  • Arye Juhász
Conference paper
Part of the Trends in Mathematics book series (TM)


The three fundamental decision problems posed by Max Dehn in 1912 are the word problem, the conjugacy problem and the isomorphism problem. Let G be a group and let u and v be elements of G. The word problem asks for an algorithm for deciding whether u = v. The conjugacy problem asks about the existence of an element gG which conjugates u to v, i.e., v = g −1 ug. A solution of the conjugacy problem clearly contains a solution of the word problem. The isomorphism problem asks whether two group presentations define isomorphic groups. The word and conjugacy problems received much attention in the literature. For a summary of results concerning the conjugacy problem until 1987 see [13] and references therein.


Word Problem Free Product Conjugacy Problem Simple Closed Curve Boundary Cycle 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Arye Juhász
    • 1
  1. 1.Department of MathematicsTechnion — Israel Institute of TechnologyHaifaIsrael

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