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- Title
On palindromic width of certain extensions and quotients of free nilpotent groups.
- Authors
Bardakov, Valeriy G.; Gongopadhyay, Krishnendu
- Abstract
In [Bardakov and Gongopadhyay, Palindromic width of free nilpotent groups, J. Algebra 402 (2014) 379-391] the authors provided a bound for the palindromic widths of free abelian-by-nilpotent group ANn of rank n and free nilpotent group n,r of rank n and step r. In the present paper, we study palindromic widths of groups and . We denote by the quotient of the group Gn = 〈x1, ..., xn〉, which is free in some variety by the normal subgroup generated by . We prove that the palindromic width of the quotient is finite and bounded by 3n. We also prove that the palindromic width of the quotient is precisely 2(n - 1). As a corollary to this result, we improve the lower bound of the palindromic width of n,r. We also improve the bound of the palindromic width of a free metabelian group. We prove that the palindromic width of a free metabelian group of rank n is at most 4n - 1.
- Subjects
PALINDROMIC DNA; QUOTIENT rings; FREE groups; GROUP theory; NILPOTENT groups; MATHEMATICAL bounds
- Publication
International Journal of Algebra & Computation, 2014, Vol 24, Issue 5, p553
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196714500246