English

Generation of polycyclic groups

Group Theory 2008-03-27 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0711.3440,
  title  = {Generation of polycyclic groups},
  author = {Martin Kassabov and Nikolay Nikolov},
  journal= {arXiv preprint arXiv:0711.3440},
  year   = {2008}
}

Comments

9 pages, some small mistakes in the first version have been corrected

R2 v1 2026-06-21T09:45:58.265Z