ON TORSION-FREE METABELIAN GROUPS WITH COMMUTATOR QUOTIENTS OF PRIME EXPONENT

Abstract

Let G be a torsion-free metabelian group having for commutator quotient, an elementary abelian p-group of rank k. It is shown that k≥3 for all primes p. Examples of such metabelian torsion-free groups are constructed for all primes p and all ranks k≥3, except for p=2, k=3.