Groups with fix-set quasi-order

Stokes, Tim E.; Hawthorn, Ian; Manoharan, Siva

Groups with fix-set quasi-order

dc.contributor.author	Stokes, Tim E.	en_NZ
dc.contributor.author	Hawthorn, Ian	en_NZ
dc.contributor.author	Manoharan, Siva	en_NZ
dc.date.accessioned	2015-11-04T22:32:36Z
dc.date.available	2015	en_NZ
dc.date.available	2015-11-04T22:32:36Z
dc.date.issued	2015	en_NZ
dc.description.abstract	If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of SX. Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.
dc.format.mimetype	application/pdf
dc.identifier.citation	Stokes, T. E., Hawthorn, I., & Manoharan, S. (2015). Groups with fix-set quasi-order. Algebra Universalis. http://doi.org/10.1007/s00012-015-0349-9	en
dc.identifier.doi	10.1007/s00012-015-0349-9	en_NZ
dc.identifier.issn	0002-5240	en_NZ
dc.identifier.uri	https://hdl.handle.net/10289/9707
dc.language.iso	en
dc.publisher	Springer Basel	en_NZ
dc.relation.isPartOf	Algebra Universalis	en_NZ
dc.rights	This is an author’s accepted version of an article published in the journal: Algebra Universalis. © 2015 Springer Basel.
dc.title	Groups with fix-set quasi-order	en_NZ
dc.type	Journal Article
pubs.begin-page	229	en_NZ
pubs.elements-id	129619
pubs.end-page	239	en_NZ
pubs.issue	3	en_NZ
pubs.notes	@article{ year={2015}, issn={0002-5240}, journal={Algebra universalis}, doi={10.1007/s00012-015-0349-9}, title={Groups with fix-set quasi-order}, url={http://dx.doi.org/10.1007/s00012-015-0349-9}, publisher={Springer Basel}, keywords={Primary: 20F99; Secondary: 20D99; 20B40; permutation group; quasi-order; lattice}, author={Hawthorn, Ian and Manoharan, Siva and Stokes, Tim}, pages={1-11}, language={English} }	en_NZ
pubs.organisational-group	/Waikato
pubs.organisational-group	/Waikato/FCMS
pubs.organisational-group	/Waikato/FCMS/Mathematics
pubs.volume	74	en_NZ