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Graduation date: 2005

Normal subgroups can be thought of as the primary building blocks for decomposing mathematicalgroups into quotient groups. The properties of the resulting quotient groups are oftenused to determine properties of the group itself. This thesis considers normal subgroups of threedimensionalcrystallographic space groups that are themselves three-dimensional crystallographicspace groups; for convenience, we refer to such a subgroup as a csg-normal subgroup. We identifypractical restrictions on csg-normal subgroups that facilitate their tabulation. First, the point groupof an csg-normal subgroup must be a normal subgroup of the crystallographic point group of thespace group, which we refer to for convenience as a cpg-normal subgroup. For each of the cpgnormalsubgroups, which are all well known, we identify the abstract quotient group. Secondly,we identify necessary conditions on the sublattice basis of any csg-normal subgroup, and tabulatethe “normally supportive“ sublattices that meet these conditions, where some tables are symbolicforms that represent infinite families of sublattices. For a given space group, every csg-normalsubgroup must be an extension of such a normally supportive sublattice, though some normallysupportive sublattices may not actually support such extensions.

6,6’-Dimethoxygossypol (DMG) is a natural product of the cotton variety Gossypium barbadense and a derivative of gossypol. Gossypol has been shown to form an abundant number of clathrates with a large variety of compounds. One of the primary reasons why gossypol can form clathrates has been because of its ability to from extensive hydrogen bonding networks due to its hydroxyl and aldehyde functional groups. Prior to this work, the only known solvate that DMG formed was with acetic acid. DMG has methoxy groups substituted at two hydroxyl positions, and consequently there is a decrease in its ability to form hydrogen bonds. Crystallization experiments were set up to see whether, like gossypol, DMG could form clathrates. The following results presented prove that DMG is capable of forming clathrates (S1 and S2) and two new polymorphs (P1 and P2) of DMG have been reported.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20164号 / 理博第4249号 / 新制||理||1611(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 池田 隆介, 教授 石田 憲二, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form $\mathbb{Z}^{n}\rtimes$G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan asks for suitable conditions for the Lyndon-Hochschild-Serre Spectral Sequence associated to this group extension to collapse at second page of the Lyndon-Hochschild-Serre spectral sequence. In this thesis we use facts from integer representation theory to reduce this problem to only considering representatives from each genus of representations, and establish techniques for constructing new examples in which the spectral sequence collapses.