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Generation of polycyclic groups

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.

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Publisher copy:
10.1515/JGT.2008.098
Journal:
Journal of Group Theory More from this journal
Volume:
12
Issue:
4
Pages:
567-577
Publication date:
2007-11-21
DOI:
EISSN:
1435-4446
ISSN:
1433-5883
Language:
English
Keywords:
Pubs id:
pubs:354379
UUID:
uuid:a7cd152d-73cd-46ec-b4d7-dd3c4f1cc358
Local pid:
pubs:354379
Source identifiers:
354379
Deposit date:
2013-11-16

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