Maximal abelian quotient of certain cyclically presented groups arising from manifolds

Abstract

The fundamental groups of certain 3−manifolds are cyclically presented. We consider the Maximal Abelian quotient, An, of the family of cyclically presented groups

that are isomorphic to the fundamental group of certain Takahashi Manifolds. We show that these Maximal Abelian quotients are 2-generated, isomorphic to and have orders where Furthermore, we prove that °(A _n ) satisfies the recurrence relation a₁ = 1, a₂ = 4h² + 4h − 1, a₃ = (3h³ + 3h − 1)², a_n = (3h² + 3h − 1)a_{n − 1} −h(3h³ + 6h² + 2h − 1)a_{n − 2} + (h(h + 1))³ for n≥4.

Keywords:

• Cyclically presented groups
• Maximal Abelian quotient
• Takahashi Manifolds