On the Bieri-Neumann-Strebel-Renz invariants of the weak commutativity construction x(G)

Author(s)

Kochloukova, Dessislava H.

• Document type: Journal article
• Source: Groups Geometry and Dynamics; v. 17, n. 1, p. 29-pg., 2023-01-01.

Abstract

For a finitely generated group G, we calculate the Bieri-Neumann-Strebel-Renz invari-ant E1(3r(G)) for the weak commutativity construction 3r(G). Identifying S(3r(G)) with S(3r(G)/ W(G)), we show E2(3r(G), Z) c E2(3r(G)/W(G), Z) and E2(3r(G)) c E2(3r(G)/W(G)), that are equalities when W(G) is finitely generated, and we explicitly calculate E2(3r(G)/ W(G), Z) and E2(3r(G)/W(G)) in terms of the E-invariants of G. We calculate completely the E-invariants in dimensions 1 and 2 of the group v(G) and show that if G is finitely generated group with finitely presented commutator subgroup then the non-abelian tensor square G (R) G is finitely presented. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants