Thesis (M.Sc.) - Carleton University, 2002. / Includes bibliographical references (p. 40-43). Also available in electronic format on the Internet.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.30).

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.

No description available.

The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.

This study investigates and evaluates the effects of an eighteen-hour weekend encounter group and three twelve-week groups--a weekly counseling group, a Bible discussion group, and a church attendance group, upon selected personality and behavioral variables, group morale and social integration. Subjects were forty-eight volunteers from a 250-member Protestant, evangelical church in a suburb of a Texas city of five-hundred thousand people. Six men and six women were randomly assigned to each of the four groups. Data analyzed were the pre-, post-, and post-post-experiment scores of the Personal Orientation Inventory, the Sixteen Personality Factor Questionnaire, and the sociometric variables based on Bonney's "Criteria for a Better Group on Sociometric Scales". The .05 level of significance was required for rejection of the null hypotheses. The statistical analyses were accomplished by applying a one-way analysis of co-variance design to the raw scores from the Personal Orientation Inventory, the Sixteen Personality Factor Questionnaire, and two of the three sociometric variables--mutual choices and opposite sex choices. The sociometric variable, choices between upper and lower quarters, was computed with the z formula. The sociometric data, mutuals and opposite sex choices on the encounter group, were further analyzed using the single-factor analysis of variance with repeated measures. It was hypothesized that the participants in the weekend encounter group would show a significantly greater change in self-actualization, positive personality and behavioral changes, social integration and group morale than would the participants in the other groups. It was further hypothesized that the weekly counseling group would show a significantly greater change in the selected variables, social integration and group morale, than would the Bible discussion or church attendance groups. It was also hypothesized that the Bible discussion group would show a significantly greater change in the selected variables, social integration and group morale than would the church attendance group. Statistical analyses failed to confirm the research hypotheses. The participants in the eighteen-hour encounter group did not show a significantly greater change in the selected personality and behavioral variables, group morale and social integration, than did the participants in the other three groups, at the conclusion of the eighteen hours or the twelve-week sessions. A partial significance was achieved by the participants in the counseling group. No significant changes were indicated by the Bible discussion or church attendance groups. The findings of this study partially support the assumption that psychological groups could enhance the ministry of the church. Therefore, it is recommended that further study on psychological-religious groups be initiated.

In this thesis we investigate the structure of locally nilpotent 5-Engel p-groups. We show that for p > 7, locally nilpotent 5-Engel p-groups have class at most 10. This is a global theorem, where the result is not dependent on the number of generators of the group. The proof uses new and established Lie methods and a custom C++ implementation of an algorithm that constructs minimal generating sets and structure constants of multi- graded Lie algebras in a variety defined by three multilinear relations, which hold in the Lie rings associated with 5-Engel p-groups. We obtain our results by calculating in the set Q(p) = {~ I x E Z, yE Z+, Y # 0 modulo any p f/. p} (where p is a set of excluded primes and x, y are arbitrarily large integers), as well as the fields Zp, p prime. We introduce several reduction theorems, making the result possible. We also present results about the normal closure of elements in these groups. We use a Higman reduction theorem and the same custom C++ program to show that locally nilpotent 5-Engel p-groups, p 2: 5, are Fitting, with Fitting degree at most 4 if p > 7, at most 5 if p = 7 and at most 6 if p = 5. These results are best possible.

In recent years. South Africa’s business and union leaders have often been called on to replicate the country’s substantial political achievements, in the economic sphere. Two important documents released in mid 1996 discuss the establishment of structures to facilitate dialogue between government, labour and business. The purpose of this would be to try to find ways of generating the growth and employment sorely needed in the country if democracy is to lead to any improvement in the living conditions of the majority. The government’s macroeconomic strategy paper - ‘Growth, Employment and Redistribution,’ commonly referred to as GEAR, was released first, followed by the report of the Labour Market Commission (LMC) convened by the President to investigate labour policy. The GEAR document proposes ‘a broad national agreement to create an environment for rapid growth, brisk investment and accelerated delivery of public services’ (1996: 26). The agreement would be needed to prevent the recent depreciation of the Rand from triggering a vicious cycle of wage and price increases which would destabilise financial markets and undermine the competitiveness of local industry. This could be achieved, GEAR argues, if labour and business were willing to consider the restraint of wages and prices. The idea of a national agreement is further elaborated in the LMC report, which proposes a ‘National Accord’ (1996). This proposal follows from the LMC’s belief that the negotiation of economic issues through institutional structures, as opposed to direct regulation by government statute, is both socially desirable and economically efficient (ibid, 219). Price restraint, wage restraint and investment decisions, together with tangible commitments from government on training, social welfare provision and industrial promotion would be the main issues covered by the accord. South Africa’s economic policy framework has been subject to heated debate since the release of GEAR. The union movement has expressed serious reservations about the market orientation of the government’s macroeconomic strategy. Given this position, together with the complex and fragmented structure of interest organisation in South Africa, the prospects for an accord or national agreement are not promising. Yet, the government has expressed the desire to set one up. This paper provides a review of political theory on interest groups. The purpose of this is to draw concepts and ideas from contributions in this area to see if they can shed any light on the nature of interest group interaction in South Africa, particularly with respect to the possibility of establishing a social accord. The review draws from two bodies of thought. The first is the theory of corporatism and the second that of public choice (often referred to as rational choice). Corporatist theory has enjoyed a fair degree of popularity amongst South African social scientists. However, the debate between them has not progressed very far, mainly due to confusion over terminology. Further, as argued Section 1, some local contributions have misread the international literature, ignoring aspects which might be of relevance to South Africa. These omissions are re-examined, but the section concludes that there are limitations in the extent to which corporatist theory is able to explain the dynamics of interest group formation and behaviour. Section 2 tries to find alternative explanations in the theory of public choice. The methodological integrity and general value of public choice theory has been strongly questioned (Green & Shapiro, 1994). While the paper provides a synopsis of public choice literature and a review of its critics, the focus is on the analysis of collective action. Despite the shortcomings which it shares with general public choice, this analysis provides useful theoretical pointers which can assist in developing an understanding of interest group dynamics which goes beyond corporatist theory. In the third section, the paper comes back to South Africa and looks at the recent history of interest organisation to establish whether any of the theoretical tools picked up in previous sections are helpful in understanding the local experience. After a general background, the section goes into the discussion of three particular issues, being: community participation in policy formation, trade policy and the labour market. Section 4 acknowledges that there is potential to build the capacity of interest organisations in South Africa and to restructure their interaction in socially beneficial ways. However, a number of issues are identified which mitigate against the conclusion of an effective social accord. These include the weaknesses evident in interest group organisation, the alliance between the African National Congress and the union federation Cosatu,1 and the absence of competition in South Africa at party political level. It is concluded that electoral reform might be a better means of democratising the country’s political environment than attempts at managing interest groups. / Working paper (South African Network for Economic Research) ; v. 1

This dissertation is devoted to the measure theoretical aspects of the theory of automata and groups generated by them. It consists of two main parts. In the first part we study the action of automata on Bernoulli measures. We describe how a finite-state automorphism of a regular rooted tree changes the Bernoulli measure on the boundary of the tree. It turns out, that a finite-state automorphism of polynomial growth, as defined by Sidki, preserves a measure class of a Bernoulli measure, and we write down the explicit formula for its Radon-Nikodim derivative. On the other hand the image of the Bernoulli measure under the action of a strongly connected finite-state automorphism is singular to the measure itself. The second part is devoted to introduction of measure into the theory of limit spaces of Nekrashevysh. Let G be a group and φ : H → G be a contracting homomorphism from a subgroup H < G of finite index. Nekrashevych associated with the pair (G, φ) the limit dynamical system (JG, s) and the limit G-space XG together with the covering ∪g∈GT · g by the tile T. We develop the theory of selfsimilar measures m on these limit spaces. It is shown that (JG, s,m) is conjugate to the one-sided Bernoulli shift. Using sofic subshifts we prove that the tile T has integer measure and we give an algorithmic way to compute it. In addition we give an algorithm to find the measure of the intersection of tiles T ∩ (T · g) for g ∈ G. We present applications to the evaluation of the Lebesgue measure of integral self-affine tiles. Previously the main tools in the theory of self-similar fractals were tools from measure theory and analysis. The methods developed in this disseration provide a new way to investigate self-similar and self-affine fractals, using combinatorics and group theory.