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An Application of Word Combinatorics to Decision Problems in Group Theory

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

Abstract

In this work we develop a graph theoretical test on graphs corresponding to subgroups of one-relator groups with small cancellation condition which, if successful, implies that the subgroup under consideration has solvable membership problem with a simple solution. The proof of the solvability of the membership problem relies on word combinatorics in an essential way.

Mathematics Subject Classification (2000)

Primary 20E06 Secondary 20F05 20F06 

Keywords

One-relator groups small cancellation conditions membership problem Whithead graphs 

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References

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    Juhász, A. A Freiheitssatz for Whitehead graphs of one-relator groups with small cancellation. Communications in Algebra 37:8, 2714–2741 (2009).zbMATHCrossRefMathSciNetGoogle Scholar
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

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

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