Short Conjugators and Compression Exponents In Free Solvable Groups

Details Short Conjugators and Compression Exponents In Free Solvable Groups Short Conjugators and Compression Exponents In Free Solvable Groups

2012-02-23

arxiv.org/abs/1202.5343v1

Mathematics

Group Theory

Scientific paper

Free solvable groups have often been studied using the Magnus embedding which, with the aid of Fox calculus, we show is a quasi-isometric embedding. In particular, we use this result to obtain a polynomial upper bound for the length of short conjugators in free solvable groups. To do this, we also need to study the same problem in wreath products in general. We also use the Magnus embedding to obtain a non-zero lower bound on $L_p$ compression exponents in free solvable groups.

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