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Palindromic width of wreath products, metabelian groups, and max-n solvable groups
Tim Riley and Andrew Sale Groups – Complexity – Cryptology, pages 121–132, 6 (2), 2014 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 \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.
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