Palindromic width of wreath products

JOURNAL OF ALGEBRA

卷:471

Article

关键词: Palindromes;    Wreath products;    Width of words;   

DOI  :  10.1016/j.jalgebra.2016.09.015

来源: Elsevier

【 摘 要 】

A palindrome is a word which reads the same left-to-right as right-to-left. We show that the wreath product G (sic) Z(n) of any finitely generated group G with Z' has finite palindromic width. This generalizes the main result from [16]. We also show that C (sic) A has finite palindromic width if C has finite commutator width and A is a finitely generated infinite abelian group. Further we prove that if H is a non-abelian group with finite palindromic width and G any finitely generated group, then every element of the subgroup G'(sic)H can be expressed as a product of uniformly boundecily many palindromes. From this we obtain that P (sic)H has finite palindromic width if P is a perfect group and further that G(sic) F has finite palindromic width for any finite, non-abelian group F. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free