Publication
The classification of normalizing groups
| dc.contributor.author | Araújo, João | |
| dc.contributor.author | Cameron, Peter J. | |
| dc.contributor.author | Mitchell, James D. | |
| dc.contributor.author | Max, Neunhöffer | |
| dc.date.accessioned | 2015-03-24T15:49:07Z | |
| dc.date.available | 2015-03-24T15:49:07Z | |
| dc.date.issued | 2013 | |
| dc.description.abstract | Let X be a finite set such that |X|=n. Let Tn and Sn denote the transformation monoid and the symmetric group on n points, respectively. Given a∈Tn∖Sn, we say that a group G⩽Sn is a-normalizing if <a,G〉∖G=〈g−1ag|g∈G>,where a, G and g−1ag | g ∈ G denote the subsemigroups of Tn generated by the sets {a} ∪ G and {g−1ag | g ∈ G}, respectively. If G is a-normalizing for all a ∈ Tn \ Sn, then we say that G is normalizing.The goal of this paper is to classify the normalizing groups and hence answer a question of Levi, McAlister, and McFadden. The paper ends with a number of problems for experts in groups, semigroups and matrix theory. | por |
| dc.identifier.citation | Araújo, João [et al.] - The classification of normalizing groups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 373 (2013), p. 1-11 | por |
| dc.identifier.doi | 10.1016/j.jalgebra.2012.08.033 | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/3812 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0021869312004930 | por |
| dc.subject | Transformation semigroups | por |
| dc.subject | Permutation groups | por |
| dc.subject | Primitive groups | por |
| dc.subject | GAP | por |
| dc.title | The classification of normalizing groups | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 11 | por |
| oaire.citation.startPage | 1 | por |
| oaire.citation.title | Journal of Algebra | por |
| person.familyName | Ribeiro Soares Gonçalves de Araújo | |
| person.givenName | João Jorge | |
| person.identifier.ciencia-id | EC1F-273A-9F24 | |
| person.identifier.orcid | 0000-0001-6655-2172 | |
| rcaap.rights | openAccess | por |
| rcaap.type | article | por |
| relation.isAuthorOfPublication | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 |