Lower central subgroups of a free group and its subgroup

Abstract

For a given free group F of arbitrary rank (possibly infinite), and its subgroup G, we address the question whether a lower central subgroup of G can contain a lower central subgroup of F. We show that the answer is no if G does not normally generate F. The question comes from a study of Hirzebruch-type invariants from iterated p-covers for three-dimensional homology cylinders.(c) World Scientific Publishing Company