Abstract
We prove that the nilpotent product of a set of groups A 1,…,A s has finite palindromic width if and only if the palindromic widths of A i ,i=1,…,s,are finite. We give a new proof that the commutator width of F n ≀K is infinite, where F n is a free group of rank n≥2 and K is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.
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Acknowledgements
The authors gratefully acknowledge the support of the Indo-Russian DST-RFBR Project Grant DST/INT/RFBR/P-137. The first author is partially supported by Laboratory of Quantum Topology of Chelyabinsk State University (Russian Federation Government Grant 14.Z50.31.0020)
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BARDAKOV, V.G., BRYUKHANOV, O.V. & GONGOPADHYAY, K. Palindromic widths of nilpotent and wreath products. Proc Math Sci 127, 99–108 (2017). https://doi.org/10.1007/s12044-016-0296-1
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DOI: https://doi.org/10.1007/s12044-016-0296-1