Palindromic width of wreath products, metabelian groups, and max-n solvable groups

Tim R. Riley; Andrew W. Sale

doi:10.1515/gcc-2014-0009

Published by De Gruyter October 7, 2014

Palindromic width of wreath products, metabelian groups, and max-n solvable groups

Tim R. Riley and Andrew W. Sale

From the journal Groups Complexity Cryptology

https://doi.org/10.1515/gcc-2014-0009

Showing a limited preview of this publication:

Abstract

A group has finite palindromic width if there exists n such that every element can be expressed as a product of n or fewer palindromic words. We show that if G has finite palindromic width with respect to some generating set, then so does G≀ℤr. We also give a new, self-contained proof that finitely generated metabelian groups have finite palindromic width. Finally, we show that solvable groups satisfying the maximal condition on normal subgroups (max-n) have finite palindromic width.

Keywords: Palindrome; metabelian group; solvable group; wreath product

MSC: 20F16; 20F65

We thank Valeriy Bardakov, Krishnendu Gongopadhyay, Elisabeth Fink, and an anonymous referee for their comments.

Received: 2014-3-12

Published Online: 2014-10-7

Published in Print: 2014-11-1

Palindromic width of wreath products, metabelian groups, and max-n solvable groups

Abstract

Journal and Issue

Articles in the same Issue