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

Adam Piggott
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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.

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Adam Piggott. 2005-04-26. Algorithmic constructions and primitive elements in the free group of rank 2. https://arxiv.org/abs/math/0504401

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