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Periodic Subwords in 2-Piece Words

C.M. Weinbaum
Journal / Anthology

Pacific Journal of Mathematics
Year: 2001
Volume: 199
Issue: 2
Page range: 493-510

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...XYX 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.

*Mathematics > Algebra > Group Theory