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Flexibility in generating sets of finite groups
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dc.contributor.author | Harper, Scott | |
dc.date.accessioned | 2022-11-08T11:30:13Z | |
dc.date.available | 2022-11-08T11:30:13Z | |
dc.date.issued | 2022-03 | |
dc.identifier | 281948046 | |
dc.identifier | bdc51558-bf09-46c2-83fc-d1022434d9bb | |
dc.identifier | 85123485282 | |
dc.identifier.citation | Harper , S 2022 , ' Flexibility in generating sets of finite groups ' , Archiv der Mathematik , vol. 118 , pp. 231-237 . https://doi.org/10.1007/s00013-021-01691-0 | en |
dc.identifier.issn | 0003-889X | |
dc.identifier.other | ORCID: /0000-0002-0056-2914/work/122216186 | |
dc.identifier.uri | https://hdl.handle.net/10023/26326 | |
dc.description.abstract | Let G be a finite group. It has recently been proved that every nontrivial element of G is contained in a generating set of minimal size if and only if all proper quotients of G require fewer generators than G. It is natural to ask which finite groups, in addition, have the property that any two elements of G that do not generate a cyclic group can be extended to a generating set of minimal size. This note answers the question. The only such finite groups are very specific affine groups: elementary abelian groups extended by a cyclic group acting as scalars. | |
dc.format.extent | 7 | |
dc.format.extent | 258702 | |
dc.language.iso | eng | |
dc.relation.ispartof | Archiv der Mathematik | en |
dc.subject | Finite grouops | en |
dc.subject | Generating sets | en |
dc.subject | Spread | en |
dc.subject | Bases | en |
dc.subject | T-NDAS | en |
dc.title | Flexibility in generating sets of finite groups | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s00013-021-01691-0 | |
dc.description.status | Peer reviewed | en |
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