Invariants of Modular Two-Row Groups

dc.contributor.authorWu, Yinglinen
dc.contributor.departmentMathematics and Statisticsen
dc.contributor.supervisorHughes, Ianen
dc.contributor.supervisorWehlau, Daviden
dc.date2009-09-29 15:08:40.705
dc.date.accessioned2009-10-06T19:50:09Z
dc.date.available2009-10-06T19:50:09Z
dc.date.issued2009-10-06T19:50:09Z
dc.degree.grantorQueen's University at Kingstonen
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-09-29 15:08:40.705en
dc.description.abstractIt is known that the ring of invariants of any two-row group is Cohen-Macaulay. This result inspired the conjecture that the ring of invariants of any two-row group is a complete intersection. In this thesis, we study this conjecture in the case where the ground field is the prime field $\mathbb{F}_p$. We prove that all Abelian reflection two-row $p$-groups have complete intersection invariant rings. We show that all two-row groups with \textit{non-normal} Sylow $p$-subgroups have polynomial invariant rings. We also show that reflection two-row groups with \textit{normal} reflection Sylow $p$-subgroups have polynomial invariant rings. As an interesting application of a theorem of Nakajima about hypersurface invariant rings, we rework a classical result which says that the invariant rings of subgroups of $\text{SL}(2,\,p)$ are all hypersurfaces. In addition, we obtain a result that characterizes Nakajima $p$-groups in characteristic $p$, namely, if the invariant ring is generated by norms, then the group is a Nakajima $p$-group.en
dc.description.degreePhDen
dc.format.extent253687 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1974/5258
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectInvariantsen
dc.subjectModularen
dc.subjectTwo-Row Groupen
dc.subjectComplete Intersectionen
dc.subjectNakajima p-Groupen
dc.titleInvariants of Modular Two-Row Groupsen
dc.typethesisen
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