Algorithmic constructions and primitive elements in the free group of rank 2

Details Algorithmic constructions and primitive elements in the free group of rank 2 Algorithmic constructions and primitive elements in the free group of rank 2

2005-04-20

arxiv.org/abs/math/0504401v2

Mathematics

Group Theory

12 pages. Replaces old version (apologies for uploading wrong version) which contained an error in the statement of Second nor

Scientific paper

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.

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