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 $G\wr {\mathbb{Z}}^r$. 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.

The example in Section 2.1 has been expanded. Otherwise only minor changes have been made. 15 pages. To appear in Groups Complexity Cryptology

References in corpus (2)

• Palindromic Automorphisms of Free Groups
• Random walks on free solvable groups

Cited by in corpus (3)

• Some Problems on Knots, Braids, and Automorphism Groups
• On palindromic width of certain extensions and quotients of free nilpotent groups
• Palindromic Width of Finitely Generated Solvable Groups