No description available.

No description available.

No description available.

Ingroup bias, which refers to people???s tendency to evaluate and treat members of their ingroups better than members of outgroups, is a central feature of intergroup relations. Conceptually, ingroup bias can be comprised of ingroup positivity, outgroup negativity, or both. However, research has often confounded these components on the assumption that they are reciprocally related. The aim of this research project was to examine the relative dominance of ingroup positivity versus outgroup negativity in ingroup bias and the relationship between them. Two approaches were employed. First, a series of laboratory studies examined the effect of threat on implicit and explicit intergroup attitudes. In Study 1, ingroup positivity and outgroup negativity were assessed in the domains of stereotyping, prejudice, and discrimination in a context where threat appeared to be salient. Analyses within and across measures revealed that ingroup positivity was more dominant than outgroup negativity, and that ingroup and outgroup attitudes were unrelated or positively related. Experiments that manipulated the salience of realistic threat (Studies 2 and 3), symbolic threat, (Studies 6 and 7), or both (Studies 4 and 5) similarly produced nonsignificant or positive correlations between ingroup and outgroup attitudes. However, in Studies 4, 5, and 7, perceptions of symbolic threat significantly influenced intergroup attitudes. Overall, the findings of the laboratory studies suggest that although threat can shift outgroup attitudes, it does not necessarily lead to reciprocity between ingroup positivity and outgroup negativity. The second approach employed in this dissertation involved content analysis of messages posted on an Internet hate site. In contrast to the laboratory experiments, Studies 8 and 9 found that ingroup positivity significantly predicted outgroup negativity. Implications of these findings are discussed, including the possibility that ingroup positivity will be linked to outgroup hostility when people are highly identified with their ingroup and when the outgroup defines the ingroup. This dissertation contributes to the intergroup relations literature by providing a more detailed account of implicit and explicit ingroup bias, and by identifying potential conditions leading to a negative relationship between ingroup and outgroup attitudes.

The main purpose of this thesis is to obtain surprising identities by counting the representations of quivers over finite fields. A classical result states that the dimension vectors of the absolutely indecomposable representations of a quiver ?? are in one-to-one correspondence with the positive roots of a root system ??, which is infinite in general. For a given dimension vector ?? ??? ??+, the number A??(??, q), which counts the isomorphism classes of the absolutely indecomposable representations of ?? of dimension ?? over the finite field Fq, turns out to be a polynomial in q with integer coefficients, which have been conjectured to be nonnegative by Kac. The main result of this thesis is a multi-variable formal identity which expresses an infinite series as a formal product indexed by ??+ which has the coefficients of various polynomials A??(??, q) as exponents. This identity turns out to be a qanalogue of the remarkable Weyl-Macdonald-Kac denominator identity modulus a conjecture of Kac, which asserts that the multiplicity of ?? is equal to the constant term of A??(??, q). An equivalent form of this conjecture is established and a partial solution is obtained. A new proof of the integrality of A??(??, q) is given. Three Maple programs have been included which enable one to calculate the polynomials A??(??, q) for quivers with at most three nodes. All sample out-prints are consistence with Kac???s conjectures. Another result of this thesis is as follows. Let A be a finite dimensional algebra over a perfect field K, M be a finitely generated indecomposable module over A ???K ??K. Then there exists a unique indecomposable module M??? over A such that M is a direct summand of M??? ???K ??K, and there exists a positive integer s such that Ms = M ??? ?? ?? ?? ??? M (s copies) has a unique minimal field of definition which is isomorphic to the centre of End ??(M???) rad (End ??(M???)). If K is a finite field, then s can be taken to be 1.

In this thesis we explore the problem of computing automorphisms of finite groups, eventually focusing on some group product constructions. Roughly speaking, the automorphism group of a group gives the nature of its internal symmetry. In general, determination of the automorphism group requires significant computational effort and it is advantageous to find situations in which this may be reduced. The two main results give descriptions of the automorphism groups of finite direct products and split metacyclic p-groups. Given a direct product G = H x K where H and K have no common direct factor, we give the order and structure of Aut G in terms of Aut H, Aut K and the central homomorphism groups Hom (H, Z(K)) and Hom (K, Z(H)). A similar result is given for the the split metacyclic p-group, in the case where p is odd. Implementations of both of these results are given as functions for the computational algebra system GAP, which we use extensively throughout. An account of the literature and relevant standard results on automorphisms is given. In particular we mention one of the more esoteric constructions, the automorphism tower. This is defined as the series obtained by repeatedly taking the automorphism group of some starting group G₀. There is interest as to whether or not this series terminates, in the sense that some group is reached that is isomorphic to its group of automorphisms. Besides a famous result of Wielandt in 1939, there has not been much further insight gained here. We make use of the technology to construct several examples, demonstrating their complex and varied behaviour. For the main results we introduce a 2 x 2 matrix description for the relevant automorphism groups, where the entries come from the homorphism groups mentioned previously. In the case of the direct product, this is later generalised to an n x n matrix (when we consider groups with any number of direct factors) and the common direct factor restriction is relaxed to the component groups not having a common abelian direct factor. In the case of the split metacyclic p-group, our matrices have entries that are not all homomorphisms, but are similar. We include the code for our GAP impementation of these results, which we show significantly expedites computation of the automorphism groups. We show that this matrix language can be used to describe automorphisms of any semidirect product and certain central products too, although these general cases are much more complicated. Specifically, multiplication is no longer defined in such a natural way as is seen in the previous cases and the matrix entries are mappings much less well-behaved than homomorphisms. We conclude with some suggestion of types of semidirect products for which our approach may yield a convenient description of the automorphisms.

Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaf 69). Also available on the World Wide Web.

The purpose of this thesis is to give a classification of anisotropic algebraic groups over number fields of higher real rank. This will complete the classification of algebraic groups over number fields of higher real rank, which was begun by V. Chernousov, L. Lifschitz and D.W. Morris in their paper "Almost-Minimal Non-Uniform Lattices of Higher Rank''. The classification of anisotropic groups of higher real rank is also used to provide a classification of uniform lattices of higher rank contained in semisimple Lie groups with no compact factors. In particular, it is shown that all such lattices sit inside Lie groups of type An. This thesis proceeds as follows: The first chapter provides motivation for the classification and introduces all the main results of the thesis. The second chapter provides relevant definitions and background material for the proof. The next chapters provide a proof of the classification theorem, with chapters 3-5 examining the absolutely simple groups and the final chapter examining the simple groups which are not absolutely simple. / Mathematics

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.