Generation of polycyclic groups
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 i...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797087222363586560 |
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| author | Kassabov, M Nikolov, N |
| author_facet | Kassabov, M Nikolov, N |
| author_sort | Kassabov, M |
| collection | OXFORD |
| 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. |
| first_indexed | 2024-03-07T02:32:44Z |
| format | Journal article |
| id | oxford-uuid:a7cd152d-73cd-46ec-b4d7-dd3c4f1cc358 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:32:44Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:a7cd152d-73cd-46ec-b4d7-dd3c4f1cc3582022-03-27T02:56:53ZGeneration of polycyclic groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a7cd152d-73cd-46ec-b4d7-dd3c4f1cc358EnglishSymplectic Elements at Oxford2007Kassabov, MNikolov, NIn 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. |
| spellingShingle | Kassabov, M Nikolov, N Generation of polycyclic groups |
| title | Generation of polycyclic groups |
| title_full | Generation of polycyclic groups |
| title_fullStr | Generation of polycyclic groups |
| title_full_unstemmed | Generation of polycyclic groups |
| title_short | Generation of polycyclic groups |
| title_sort | generation of polycyclic groups |
| work_keys_str_mv | AT kassabovm generationofpolycyclicgroups AT nikolovn generationofpolycyclicgroups |