Generation of polycyclic groups

Details Generation of polycyclic groups Generation of polycyclic groups

2007-11-21

arxiv.org/abs/0711.3440v2

Mathematics

Group Theory

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

Scientific paper

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.

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