by Au Pat Nien. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 86-88). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Valuations --- p.4 / Chapter 2.1 --- Preliminaries --- p.4 / Chapter 2.2 --- Complete Fields --- p.6 / Chapter 2.3 --- Unramified Extension of Complete Field --- p.10 / Chapter 2.4 --- Local Fields --- p.12 / Chapter 3 --- Ramification Groups and Hasse-Herbrand Function --- p.16 / Chapter 3.1 --- Ramification Groups --- p.16 / Chapter 3.2 --- "The Quotients Gi/Gi+1, i ≥ 0" --- p.17 / Chapter 3.3 --- The Hasse-Herbrand function --- p.19 / Chapter 4 --- The Norm Map --- p.21 / Chapter 4.1 --- Lemmas --- p.21 / Chapter 4.2 --- The Norm Map on the Residue Field of a Totally Ramified Extension of Prime Degree --- p.22 / Chapter 4.3 --- Extension of the Perfect Residue Field in a Totally Ramified Extension --- p.26 / Chapter 4.4 --- The Norm Map on Finite Separable Extension of Knr with K Perfect --- p.28 / Chapter 5 --- Cohomology of Finite Groups --- p.30 / Chapter 5.1 --- Preliminaries --- p.30 / Chapter 5.2 --- Mappings of Cohomology Groups --- p.32 / Chapter 5.2.1 --- Restriction and Inflation --- p.32 / Chapter 5.2.2 --- Corestriction --- p.34 / Chapter 5.3 --- Cup Product --- p.34 / Chapter 5.4 --- Cohomology Groups of Low Dimensions --- p.35 / Chapter 5.5 --- Some Results of Group Cohomology --- p.43 / Chapter 6 --- The Brauer Group of a Field --- p.57 / Chapter 7 --- The Norm Residue Map --- p.60 / Chapter 7.1 --- Determination of the Brauer Group of a Local Field --- p.60 / Chapter 7.2 --- Canonical Class --- p.62 / Chapter 7.3 --- The Reciprocity Law --- p.64 / Chapter 8 --- The Local Symbol --- p.74 / Chapter 8.1 --- Definition --- p.74 / Chapter 8.2 --- The Hilbert Symbol --- p.74 / Chapter 8.3 --- The Differential of the Formal Power Series --- p.76 / Chapter 8.4 --- The Artin-Schreier Symbol --- p.78 / Chapter 9 --- Characterization of a Norm Group --- p.81 / Bibliography

Lam Chi Ming. / Thesis submitted in: August 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 47-48). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Introduction to Real Groups and Real representa- tions --- p.6 / Chapter 1.1 --- Real Groups and Real representations --- p.6 / Chapter 1.2 --- "RR(G, ε)" --- p.10 / Chapter 1.3 --- Examples of Real representations --- p.15 / Chapter 1.3.1 --- Cyclic groups --- p.17 / Chapter 1.3.2 --- Dihedral groups --- p.18 / Chapter 1.3.3 --- Other examples --- p.19 / Chapter 2 --- Brauer induction Theorem on Real representations --- p.22 / Chapter 2.1 --- Real induction --- p.22 / Chapter 2.2 --- p-hyperelementary subgroups --- p.27 / Chapter 2.3 --- Brauer induction Theorem on Real Representations --- p.29 / Chapter 2.4 --- Monomial Real Representations --- p.42 / Bibliography --- p.47

The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) as a homomorphic image of the progenitor 2^(*15) : (15x4), we obtain the group PGL(2; 7) as a homomorphic image of the progenitor 2^7 : D_14, we obtain the group S_6 as a homomorphic image of the progenitor 2^5 : (5 : 4), and we obtain the group S_7 as a homomorphic image of the progenitor 2^(*15) : (15 : 4). Also, have given some unsuccessful progenitors.

We construct an algorithm for getting a reduced expression for any element in a complex reflection group G(m, 1, r) by sorting the element, which is in the form of a sequence of complex numbers, to the identity. Thus, the algorithm provides us a set of reduced expressions, one for each element. We establish a one-one correspondence between the set of all reduced expressions for an element and a set of certain sorting sequences which turn the element to the identity. In particular, this provides us with a combinatorial method to check whether an expression is reduced. We also prove analogues of the exchange condition and the strong exchange condition for elements in a G(m, 1, r). A Bruhat order on the groups is also defined and investigated. We generalize the Geck-Pfeiffer reducibility theorem for finite Coxeter groups to the groups G(m, 1, r). Based on this, we prove that a character value of any element in an Ariki-Koike algebra (the Hecke algebra of a G(m, 1, r)) can be determined by the character values of some special elements in the algebra. These special elements correspond to the reduced expressions, which are constructed by the algorithm, for some special conjugacy class representatives of minimal length, one in each class. Quasi-parabolic subgroups are introduced for investigating representations of Ariki- Koike algebras. We use n x n arrays of non-negative integer sequences to characterize double cosets of quasi-parabolic subgroups. We define an analogue of permutation modules, for Ariki-Koike algebras, corresponding to certain subgroups indexed by multicompositions. These subgroups are naturally corresponding, not necessarily one-one, to quasi-parabolic subgroups. We prove that each of these modules is free and has a basis indexed by right cosets of the corresponding quasi-parabolic subgroup. We also construct Murphy type bases, Specht series for these modules, and establish a Young's rule in this case.

This thesis deals with the study of baryon spectra in the context of the $1/N_c$ expansion. The standard tool to study baryon properties is the constituent quark model. The results are naturally model dependent. The $1/N_c$ expansion generates a new perturbative approach to QCD, convenient for low momentum transfer. It provides a new theoretical method that is quantitative, systematic and predictive. In the first part of the thesis, the $1/N_c$ expansion is introduced as well as the baryon structure at large $N_c$. A summary of important results for ground-state baryons is provided. The second part of the thesis is devoted to excited baryon states. The symmetric orbital states are treated by analogy to the ground state. For mixed symmetric states, two approaches are presented. The traditional one starts from the decoupling of the wave function into an excited quark and a symmetric core. To make the problem tractable the wave function is treated approximately, justified by a Hartree scheme. This approach is applied to the study of the $[{f 70},ell^+] (ell=0,2)$ multiplets (nonstrange and strange cases) and of the $[{f 56},4^+]$ multiplet. An important physical result is the dependence of the spin dependent terms of the mass operator on the excitation energy. Recently we suggested a new approach based on a rigorous group theoretical treatment of the matrix elements of SU(4). No decoupling and no approximations are necessary. When applied to the $[{f 70},1^-]$ nonstrange multiplet, it is found that the leading corrections to the mass operator are of order $1/N_c$ instead of $N_c^0$, as predicted by the decoupling procedure.

Thesis (Ph. D.)--Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 59-60). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 65-68).

Not available / text

Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.

No description available.