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

2013/07/18 by T. R. Riley, Riley, T. R., A. W. Sale +1
Mathematics · #20F16 #20F65 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F16 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1307.4861

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

arxiv created 2014/09/12 · arxiv updated 2014/09/16

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 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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