A subgroup theorem for free nilpotent groups

A Subgroup Theorem for Free Products of Pro-Finite Groups

The notion of a free product of pro-finite groups has some important applications in the theory of algebraic number fields (see [3]). In this connection, it is interesting to get some knowledge about the subgroups of such a free product. The aim of this paper is to show a theorem for the open subgroups of a free pro-finite product, which is an analog of Kurosh’s wellknown subgroup theorem for t...

Normal subgroup growth in free class-2-nilpotent groups

Let F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions ζ F2,d(s), prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

A Torus Theorem for Homotopy Nilpotent Groups

Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant we compare with classical cocategory, but also with the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to character...

A Paley-Wiener Like Theorem for Nilpotent Lie Groups

A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.