Atlas: Infinite words and length functions on groups by Denis Serbin

Atlas home || Conferences | Abstracts | about Atlas

G^3 = Geometric Group Theory on the Gulf Coast
March 15-17, 2002
The University of New Orleans and the University of South Alabama
New Orleans, LA, USA

Organizers
Stephen Brick, Craig Jensen, Igor Mineyev

View Abstracts
Conference Homepage

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

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: March 4, 2002