Dimension subgroups of metabelian p-groups (Q1105691)

It is shown that if G is a metabelian p-group and \(D_ n(G)\) is the n-th dimension subgroup of G over the integers, then \(D_ n(G)\) coincides with the n-th term of the lower central series of G for \(n\leq 2p-1\). This is an improvement of previous work of the author on dimension subgroups of metabelian groups, and is proved by a finely balanced combination of techniques from the author's previous work with ideas of \textit{J. Sjogren} [ibid. 14, 175-194 (1979; Zbl 0395.20019)], as simplified by \textit{G. Cliff} and the reviewer [ibid. 47, 231-242 (1987; Zbl 0633.20004)]. The introduction contains a brief account of other work on dimension subgroups, particularly in the metabelian case.