Infinite words and length functions on groups
by
Denis Serbin
Grad. Ctr., City University of New York
Coauthors: Alexei Miasnikov (City University of New York), Vladimir Remeslennikov (Omsk State University, Russia)

Let X be an alphabet and A be a discretely ordered abelian group. We consider the set of sequences w: [1, f_w] --> X ^{+/- 1} defined on closed intervals [1, f_w], f_w >= 0 in A⁺ and derive some interesting properties of it. In particular, if Z[t] is the ring of integer polynomials Z[t] then elements of Lyndon's free Z[t]-group F(X)^Z[t] can be represented by such sequences over the the additive group of Z[t]. This gives a regular free Lyndon's length function w --> f_w on F(X)^Z[t] with values in Z[t]⁺. This construction is very natural and provides a new method to construct length functions on various groups. Further generalizations also will be discussed.

Date received: February 14, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-75.