• Palindromic widths of nilpotent and wreath products

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/127/01/0099-0108

• Keywords

Palindromic width; commutator width; wreath products; nilpotent product.

• Abstract

We prove that the nilpotent product of a set of groups $A_1, \ldots , A_s$ has finite palindromic width if and only if the palindromic widths of $A_i$, $i = 1, \ldots , s$, are finite. We give a new proof that the commutator width of $F_n \wr K$ is infinite, where $F_n$ is a free group of rank $n\geq 2$ 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.

• Author Affiliations

1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk 630090, Russia and Laboratory of Quantum Topology, Chelyabinsk State University, Brat'ev Kashirinykh Street 129, Chelyabinsk 454001, Russia
2. Siberian University of Consumer Cooperatives, Novosibirsk 630087, Russia
3. Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, S.A.S. Nagar, P.O. Manauli 140 306, India

• Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019