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

Palindromic width of wreath products, metabelian groups, and max-n solvable groups 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 ≀ ℤ r \$G \wr \mathbb {Z}^{r}\$ . 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

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

, Volume 6 (2) – Nov 1, 2014
12 pages

/lp/de-gruyter/palindromic-width-of-wreath-products-metabelian-groups-and-max-n-X9MhnoFgEY
Publisher
de Gruyter
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2014-0009
Publisher site
See Article on Publisher Site

### Abstract

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 ≀ ℤ r \$G \wr \mathbb {Z}^{r}\$ . 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.

### Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2014