2020/10/25 by Dessislava H. Kochloukova, Kochloukova, Dessislava H.
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2010.13041
openalex publication_date 2020/10/25 · openalex created_date 2020/10/29 · openalex updated_date 2026/07/28
For a finitely generated group G we calculate the Bieri-Neumann-Strebel-Renz invariant Σ1(\X(G)) for the weak commutativity construction \X(G). Identifying S(\X(G)) with S(\X(G) / W(G)) we show Σ2(\X(G),\Z) ⊆ Σ2(\X(G)/ W(G),\Z) and Σ2(\X(G)) ⊆ Σ2(\X(G)/ W(G)) that are equalities when W(G) is finitely generated and we explicitly calculate Σ2(\X(G)/ W(G),\Z) and Σ2(\X(G)/ W(G)) in terms of the Σ-invariants of G. We calculate completely the Σ-invariants in dimensions 1 and 2 of the group ν(G) and show that if G is finitely generated group with finitely presented commutator subgroup then the non-abelian tensor square G ⊗ G is finitely presented.