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

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.

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

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