2005/04/20 by Adam Piggott, Piggott, Adam
Mathematics · #20E05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E05
paper · pdf · doi:10.48550/arxiv.math/0504401
12 pages. Replaces old version (apologies for uploading wrong version) which contained an error in the statement of Second normal form theorem
arxiv created 2005/04/26 · arxiv updated 2009/12/01
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.