dc.contributor.author Wu, Yinglin dc.contributor.other Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) en dc.date 2009-09-29 15:08:40.705 en dc.date.accessioned 2009-10-06T19:50:09Z dc.date.available 2009-10-06T19:50:09Z dc.date.issued 2009-10-06T19:50:09Z dc.identifier.uri http://hdl.handle.net/1974/5258 dc.description Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-09-29 15:08:40.705 en dc.description.abstract It is known that the ring of invariants of any two-row group is Cohen-Macaulay. en 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. dc.format.extent 253687 bytes dc.format.mimetype application/pdf dc.language en en dc.language.iso en en dc.relation.ispartofseries Canadian theses en dc.rights This 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.subject Invariants en dc.subject Modular en dc.subject Two-Row Group en dc.subject Complete Intersection en dc.subject Nakajima p-Group en dc.title Invariants of Modular Two-Row Groups en dc.type Thesis en dc.description.degree Ph.D en dc.contributor.supervisor Hughes, Ian en dc.contributor.supervisor Wehlau, David en dc.contributor.department Mathematics and Statistics en
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