Preprint

nilpotent groups with balanced presentations. II

J. A. Hillman


Abstract

Let G be a nilpotent group with a balanced presentation. Then either GZ3 or β1(G;Q)2. We show that if G has an abelian normal subgroup A such that G/AZ2 then G is torsion-free and has Hirsch length h(G)4. We also consider the torsion subgroup of G when h(G)2.

Keywords: balanced, nilpotent, Hirsch length, metabelian.

AMS Subject Classification: Primary 20F18; secondary 20J05, 57N13.

This paper is available as a pdf (324kB) file. It is also on the arXiv: arxiv.org/abs/2107.09985.

Tuesday, May 31, 2022