Subgroups of finitely presented metabelian groups of finite rank

Abstract

Let G be a finitely generated metabelian group whose derived group G′ has finite rank. It is shown that G can be embedded in a finitely presented metabelian group H with H′ of finite rank.

Subgroups of Finitely Presented Centre-by-Metabelian Groups

“…(see [9] for unexplained terminology). In particular, we see that a finitely generated metabelian group of finite Prufer rank can be embedded into a finitely presented metabelian group of finite Prufer rank, a result first proved by J. Boler [4].…”