Algorithmic constructions and primitive elements in the free group of rank 2
Group Theory
2007-05-23 v2
Abstract
The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from an elementary algorithm for constructing a primitive element p in F(x, y) with a given exponent sum pair (X, Y), if such an element p exists. Several results concerning the primitive elements of F(x, y) are recast as applications of the algorithm and the normal form.
Keywords
Cite
@article{arxiv.math/0504401,
title = {Algorithmic constructions and primitive elements in the free group of rank 2},
author = {Adam Piggott},
journal= {arXiv preprint arXiv:math/0504401},
year = {2007}
}
Comments
12 pages. Replaces old version (apologies for uploading wrong version) which contained an error in the statement of Second normal form theorem