The groups of two classes of certain cyclically presented groups are essentially 3-generated

Abstract

Two classes of cyclically presented groups were introduced in [3] and proven infinite for n \(\succeq\) 3 in [2].  I show that the groups of these classes of certain cyclically presented groups are essentially 3-generated.  The groups G_n and H_n for n = 3 and 4 were shown to be 2-generated in [9] and [1], while the abelianized groups \(G_n^{ab}\) of G_n were dealt with in [8].  Naturally, the groups G_n and H_n for n = 1 and 2 are trivial.  Showing that the groups of these two classes are essentially 3-generated has been the most diffcult to solve thus far.