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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

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2014-0009
Publisher site
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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 Cryptology – de Gruyter

Published: Nov 1, 2014

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