Generation of polycyclic groups
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In this note we give an alternative proof of a theorem of Linnell and Warhurst that the number of generators d(G) of a polycyclic group G is at most d(\hat G), where d(\hat G) is the number of generators of the profinite completion of G. While not claiming anything new we believe that our argument is much simpler that the original one. Moreover our result gives some sufficient condition when d(G)=d(\hat G) which can be verified quite easily in the case when G is virtually abelian.
9 pages, some small mistakes in the first version have been corrected
9 pages, some small mistakes in the first version have been corrected