Extension of a Schur theorem to groups with a central factor with a bounded section rank. (Q2438378)

In this interesting article, the authors generalize a well known classical I. Schur result which states that the derived subgroup of a group is finite provided its central factor is finite. Namely, they show that if the \(p\)-section rank of the central factor of a locally generalized radical group is bounded, then so is the \(p\)-section rank of its derived subgroup. The main result is the following: There exists a function \(\lambda_2\) such that if \(G\) is a locally generalized radical group and \(C\) is a central subgroup such that \(G/C\) has section \(p\)-rank \(s\), then \(r_p([G,G])\leq\lambda_2(s)\).