On Some Embedment of Groups into Wreath Products

Distortion of Wreath Products in Some Finitely Presented Groups

Wreath products such as Z ≀ Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z ≀ Z as a subgroup of Thompson’s group F and as a subgroup of Baumslag’s metabelian group G. We find that Z ≀ Z is undistorted in F but is at least exponentially distorted in G.

Growth Series of Some Wreath Products

The growth series of certain finitely generated groups which are wreath products are investigated. These growth series are intimately related to the traveling salesman problem on certain graphs. A large class of these growth series is shown to consist of irrational algebraic functions. 0. Introduction Let r be a group with a finite generating set S. Define the S'-length \\g\\s of an element g i...

Two Problems on Varieties of Groups Generated by Wreath Products

Group Codes based on Wreath Products of Complex Reflection Groups

Group codes based on wreath products of complex matrix groups are constructed. Efficient algorithms for encoding and decoding these codes are described.

Wreath Products and Existentially Complete Solvable Groups

It is known that the theory of abelian groups has a model companion but that the theory of groups does not. We show that for any fixed 22 a 2 the theory of groups solvable of length s 22 has no model companion. For the metabelian case (22 = 2) we prove the stronger result that the classes of finitely generic, infinitely generic, and existentially complete metabelian groups are all distinct. We ...