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We prove a ∑-version of the result of Bieri, Neumann and Strebel [R. Bieri, W. D. Neumann and R. Strebel. A geometric invariant of discrete groups.  Invent. Math.  90  (1987), 451–477] that for a finitely presented group  G  without free subgroups of rank 2 the set ∑ 1 ( G )  c   has no antipodal points. More precisely, we prove that for such a group  G

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