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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/130/0022

    • Keywords

       

      Palindromic width; graph of groups; HNN extension; amalgamated free product

    • Abstract

       

      In this paper, we answer questions raised by Bardakov and Gongopadhyay (Commun. Algebra 43(11) (2015) 4809–4824). We prove that the palindromic width of HNN extension of a group by proper associated subgroups is infinite. We also prove that the palindromic width of the amalgamated free product of two groups via a proper subgroup is infinite (except when the amalgamated subgroup has index two in each of the factors). Combining these results it follows that the palindromic width of the fundamental group of a graph of groups is mostly infinite.

    • Author Affiliations

       

      KRISHNENDU GONGOPADHYAY1 SWATHI KRISHNA1

      1. Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, S.A.S. Nagar, Punjab 140 306, India

    • Dates

       
      Published
      20 February 2020
      Manuscript received
      21 September 2018
      Manuscript revised
      28 June 2019
      Accepted
      10 August 2019
      Early published
      Unedited version published online
      Final version published online
      15 February 2020

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