No description available.

The purpose of this paper was to find a general formula to count the number of automorphisms of any finite abelian group. These groups were separated into five different types. For each of the first three types, theorems were proven, and formulas were derived based on the theorems. A formula for the last two types of groups was derived from a theorem based on a conjecture which was proven in only one direction. Then it was shown that a count found from any of the first three formulas could also be found using the last formula. The result of these comparisons gave credence to the conjecture. Thus we found that the last formula is a general formula to count the number of automorphisms of finite abelian groups. / Department of Mathematical Sciences

Dated 1983 / Bibliography: leaves 143-145 / 145 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, 1984

Thesis (M. Sc.)--Carleton University, 2004. / Includes bibliographical references (p. 56-57). Also available in electronic format on the Internet.

Thesis (doctoral)--Universität Bonn, 1988. / Includes bibliographical references.

No description available.

Nous déterminons dans cette thèse l'image des groupes de Artin associés à des groupes de Coxeter irréductibles dans leur algèbre de Iwahori-Hecke finie associée. Cela a été fait en type A dans des articles de Brunat, Marin et Magaard. Dans le cas générique, la clôture de l'image de Zariski a été déterminée dans tous les cas par Marin. L'approximation forte suggère que les résultats devraient être similaire dans le cas fini. Il est néanmoins impossible d'utiliser l'approximation forte sans utiliser de lourdes hypothèses et limiter l'étendue des résultats. Nous démontrons dans cette thèse que les résultats sont similaires mais que de nouveaux phénomènes interviennent de par la complexification des extensions de corps considérées. Les arguments principaux proviennent de la théorie des groupes finis. Nous utiliserons notamment un Théorème de Guralnick et Saxl qui utilise la classification des groupes finis simples pour les représentations de hautes dimensions. Ce théorème donne des conditions pour que des sous-groupes de groupes linéaires soient des groupes classiques dans une représentation naturelle. En petite dimension, nous utiliserons la classification des sous-groupes maximaux des groupes classiques de Bray, Holt et Roney-Dougal pour les cas les plus compliqués / In this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in type A in articles by Brunat, Marin and Magaard. The Zariski closure of the image was determined in the generic case by Marin. It is suggested by strong approximation that the results should be similar in the finite case. However, the conditions required to use are much too strong and would only provide a portion of the results. We show in this thesis that they are but that new phenomena arise from the different field factorizations. The techniques used in the finite case are very different from the ones in the generic case. The main arguments come from finite group theory. In high dimension, we will use a theorem by Guralnick-Saxl which uses the classification of finite simple groups to give a condition for subgroups of linear groups to be classical groups in a natural representation. In low dimension, we will mainly use the classification of maximal subgroups of classical groups obtained by Bray, Holt and Roney-Dougal for the complicated cases

No description available.

Let G be a finite group. Given a contravariant, product preserving functor F:G-sets → AB, we construct a Green-functor A(F):G-sets → CRNG which specializes to the Burnside ring functor when F is trivial. A(F) permits a natural addition and multiplication between elements in the various groups F(S), S ∈ G-sets. If G is the Galois group of a field extension L/K, and SEP denotes the category of K-algebras which are isomorphic with a finite product of subfields of L, then any covariant, product preserving functor ρ:SEP → AB induces a functor Fᵨ:G → AB, and thus the Green-functor Aᵨ may be obtained. We use this observation for the case ρ = Br, the Brauer group functor, and show that Aᵦᵣ(G/G) is free on K-algebra isomorphism classes of division algebras with center in SEP. We then interpret the induction theory of Mackey-functors in this context. For a certain class of functors F, the structure of A(F) is especially tractable; for these functors we deduce that (DIAGRAM OMITTED), where the product is over isomorphism class representatives of transitive G-sets. This allows for the computation of the prime ideals of A(F)(G/G), and for an explicit structure theorem for Aᵦᵣ, when G is the Galois group of a p-adic field. We finish by considering the case when G = Gal(L/Q), for an arbitrary number field L.

Guo Xiuyun. / "May 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 103-108) and index. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.