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18.5 (2014)

Open

Let the (soluble) group $G = AB$ with finite torsion-free rank $r_0(G)$ be the product of two subgroups $A$ and $B$. Is the equation $r_0(G) = r_0(A) + r_0(B) - r_0(A \cap B)$ valid in this case? It is known that the inequality $\leqslant$ always holds.

Contributor: B. Amberg

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