Twisted Burnside Theory for the Discrete Heisenberg Group and for Wreath Products of Some Groups

TL;DR

This paper proves the RP-property for wreath products of finitely generated Abelian groups with integers, providing the first example of finitely generated RP-groups that are not almost polycyclic.

Contribution

It introduces a new application of twisted Burnside theory to wreath products, expanding understanding of RP-groups beyond almost polycyclic cases.

Findings

RP-property established for specific wreath products

First known finitely generated RP-groups not almost polycyclic

Advances in twisted Burnside theory for group analysis

Abstract

The RP-property of Fel'shtyn and Troitsky is proved for wreath products of finitely generated Abelian groups with the group of integers. Such wreath products become the first known example of finitely generated RP-groups being not almost polycyclic.