The palindromic width of a free product of groups

Author:

Bardakov Valery,Tolstykh Vladimir

Abstract

AbstractPalindromes are those reduced words of free products of groups that coincide with their reverse words. We prove that a free product of groups G has infinite palindromic width, provided that G is not the free product of two cyclic groups of order two (Theorem 2.4). This means that there is no uniform bound k such that every element of G is a product of at most k palindromes. Earlier, the similar fact was established for non-abelian free groups. The proof of Theorem 2.4 makes use of the ideas by Rhemtulla developed for the study of the widths of verbal subgroups of free products.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Palindromic width of graph of groups;Proceedings - Mathematical Sciences;2020-02-15

2. Palindromic widths of nilpotent and wreath products;Proceedings - Mathematical Sciences;2016-07-29

3. Palindromic Width of Finitely Generated Solvable Groups;Communications in Algebra;2015-07-21

4. SOME PROBLEMS ON KNOTS, BRAIDS, AND AUTOMORPHISM GROUPS;SIB ELECTRON MATH RE;2015

5. On palindromic width of certain extensions and quotients of free nilpotent groups;International Journal of Algebra and Computation;2014-08

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