Subgroups of constructive nilpotent-by-abelian groups and a generalization of a result of Bieri, Neumann and Strebel

Abstract

W e prove a Σ - v e r s i o n o f the result o f B i e r i , Neumann and S t r e b e l [ 6 ] that f o r a fi¬ n i t e l y presented group G without f r e e subgroups o f rank 2 the s e t Σ1(G)c has no antipodal points. More p r e c i s e l y , w e prove that f o r s u c h a group G