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

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.

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The character table of a finite group is a very powerful tool to study the groups and to prove many results. Any finite group is either simple or has a normal subgroup and hence will be of extension type. The classification of finite simple groups, more recent work in group theory, has been completed in 1985. Researchers turned to look at the maximal subgroups and automorphism groups of simple groups. The character tables of all the maximal subgroups of the sporadic simple groups are known, except for some maximal subgroups of the Monster M and the Baby Monster B. There are several well-developed methods for calculating the character tables of group extensions and in particular when the kernel of the extension is an elementary abelian group. Character tables of finite groups can be constructed using various theoretical and computational techniques. In this thesis we study the method developed by Bernd Fischer and known nowadays as the theory of Clifford-Fischer matrices. This method derives its fundamentals from the Clifford theory. Let G = N·G, where N C G and G/N = G, be a group extension. For each conjugacy class [gi]G, we construct a non-singular square matrix Fi, called a Fischer matrix. Once we have all the Fischer matrices together with the character tables (ordinary or projective) and fusions of the inertia factor groups into G, the character table of G is then can be constructed easily. In this thesis we apply the coset analysis technique (this is a method to find the conjugacy classes of group extensions) together with theory of Clifford-Fischer matrices to calculate the ordinary character tables of seven groups of extensions type, in which four are non-split and three are split extensions. These groups are of the forms: 21+8 + ·A9, 37:Sp(6, 2), 26·Sp(6, 2), 25·GL(5, 2), 210:(U5(2):2), 21+6 − :((31+2:8):2) and 22n·Sp(2n, 2) and 28·Sp(8, 2). In addition we give some general results on the non-split group 22n·Sp(2n, 2). / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

The purpose of this thesis is to discuss the rôle of certain types of quiver which appear in the modular representation theory of finite groups. It is our concern to study two different types of quiver. First of all we construct the ordinary quiver of certain blocks of defect 2 of the symmetric group, and then apply our results to the alternating group and to the theory of partitions. Secondly, we consider connected components of the stable Auslander-Reiten quiver of certain groups G with normal subgroup N. The main interest lies in comparing the tree class of components of N-modules, with the tree class of components of these modules induced up to G.

[Truncated abstract] A matrix is said to be cyclic if its characteristic polynomial is equal to its minimal polynomial. Cyclic matrices play an important role in some algorithms for matrix group computation, such as the Cyclic Meataxe of Neumann and Praeger. In 1999, Wall and Fulman independently proved that the proportion of cyclic matrices in general linear groups over a finite field of fixed order q has limit [formula] as the dimension approaches infinity. First we study cyclic matrices in maximal reducible matrix groups, that is, the stabilisers in general linear groups of proper nontrivial subspaces. We modify Wall’s generating function approach to determine the limiting proportion of cyclic matrices in maximal reducible matrix groups, as the dimension of the underlying vector space increases while that of the invariant subspace remains fixed. This proportion is found to be [formula] note the change of the exponent of q in the leading term of the expansion. Moreover, we exhibit in each maximal reducible matrix group a family of noncyclic matrices whose proportion is [formula]. Maximal completely reducible matrix groups are the stabilisers in a general linear group of a nontrivial decomposition U1⊕U2 of the underlying vector space. We take a similar approach to determine the limiting proportion of cyclic matrices in maximal completely reducible matrix groups, as the dimension of the underlying vector space increases while the dimension of U1 remains fixed. This limiting proportion is [formula]. ... We prove that this proportion is[formula] provided the dimension of the fixed subspace is at least two and the size q of the field is at least three. This is also the limiting proportion as the dimension increases for separable matrices in maximal completely reducible matrix groups. We focus on algorithmic applications towards the end of the thesis. We develop modifications of the Cyclic Irreducibility Test - a Las Vegas algorithm designed to find the invariant subspace for a given maximal reducible matrix algebra, and a Monte Carlo algorithm which is given an arbitrary matrix algebra as input and returns an invariant subspace if one exists, a statement saying the algebra is irreducible, or a statement saying that the algebra is neither irreducible nor maximal reducible. The last response has an upper bound on the probability of incorrectness.

Thesis (Ph.D.)--University of Western Australia, 2006.

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 121-125). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (M. Sc.)--Carleton University, 2003. / Includes bibliographical references (p. 36-37). Also available in electronic format on the Internet.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, University of Glasgow, 2008. Includes bibliographical references. Print version also available.