dc.contributor.author | Mitchell, James D. | |
dc.contributor.author | Morayne, Michal | |
dc.contributor.author | Peresse, Yann | |
dc.date.accessioned | 2017-04-20T16:00:38Z | |
dc.date.available | 2017-04-20T16:00:38Z | |
dc.date.issued | 2010-09-21 | |
dc.identifier.citation | Mitchell , J D , Morayne , M & Peresse , Y 2010 , ' GENERATING THE INFINITE SYMMETRIC GROUP USING A CLOSED SUBGROUP AND THE LEAST NUMBER OF OTHER ELEMENTS ' , Proceedings of the American Mathematical Society , vol. 139 , no. 2 . < http://www.ams.org/journals/proc/2011-139-02/S0002-9939-2010-10694-9/S0002-9939-2010-10694-9.pdf > | |
dc.identifier.issn | 0002-9939 | |
dc.identifier.uri | http://hdl.handle.net/2299/17992 | |
dc.description | J. D. Mitchell, M. Morayne, and Y. Peresse, 'Generating the infinite symmetric group using a closed subgroup and the least number of other elements', Proceedings of te American Mathematical Society, Vol. 139 (2): 401-405, February 2011, version of record available online at http://www.ams.org/journals/proc/2011-139-02/S0002-9939-2010-10694-9/S0002-9939-2010-10694-9.pdf. © 2010 American Mathematical Society. | |
dc.description.abstract | Let S∞ denote the symmetric group on the natural numbers N. Then S∞ is a Polish group with the topology inherited from NN with the product topology and the discrete topology on N. Let d denote the least cardinality of a dominating family for NN and let c denote the continuum. Using theorems of Galvin, and Bergman and Shelah we prove that if G is any subgroup of S∞ that is closed in the above topology and H is a subset of S∞ with least cardinality such that G ∪ H generates S∞, then |H|∈{0, 1, d,c}. | en |
dc.language.iso | eng | |
dc.relation.ispartof | Proceedings of the American Mathematical Society | |
dc.subject | Group Theory | |
dc.subject | Topological Algebra | |
dc.subject | Infinite Combinatorics | |
dc.title | GENERATING THE INFINITE SYMMETRIC GROUP USING A CLOSED SUBGROUP AND THE LEAST NUMBER OF OTHER ELEMENTS | en |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://www.ams.org/journals/proc/2011-139-02/S0002-9939-2010-10694-9/S0002-9939-2010-10694-9.pdf | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |