Periodic subwords in 2-piece words

C.M. Weinbaum

Vol. 199 (2001), No. 2, 493–510

DOI: 10.2140/pjm.2001.199.493

Abstract

We find families of words W where W is a product of k pieces for k = 2. For k = 3,4,6, W arises in a small cancellation group with single defining relation W = 1. We assume W involves generators but not their inverses and does not have a periodic cyclic permutation (like XY …XY X for nonempty base word XY ). We prove W or W written backwards equals ABCD, where ABC, CDA are periodic words with base words of different lengths. One family includes words of the form EFGG for periodic words G, E, F with the same base word and increasing lengths. Other W are found using Mathematica.

Milestones

Received: 17 May 1999

Revised: 10 April 2000

Published: 1 June 2001