Triply factorized groups

Rank formulae for factorized groups

The following inequalities for the torsion-free rank r0(G) of the group G=AB and for the p∞-rank rp(G) of the soluble-by-finite group G=AB are stated: $$\begin{gathered} r_0 (G) \leqslant r_0 (A) + r_0 (B) - r_0 (A \cap B), \hfill \\ r_p (G) \leqslant r_p (A) + r_p (B) - r_p (A \cap B). \hfill \\ \end{gathered} $$

On trifactorized soluble minimax groups