Palindromic widths of nilpotent and wreath products |
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| Authors: | VALERIY G BARDAKOV OLEG V BRYUKHANOV KRISHNENDU GONGOPADHYAY |
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| Institution: | 1.Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk 630090, Russia and Laboratory of Quantum Topology,Chelyabinsk State University,Chelyabinsk,Russia;2.Siberian University of Consumer Cooperatives,Novosibirsk,Russia;3.Department of Mathematical Sciences,Indian Institute of Science Education and Research (IISER) Mohali,Knowledge City,India |
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| 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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