Reflections in abstract Coxeter groups

Let $W$ be a Coxeter group and $r\in W$ a reflection. If the group of order 2 generated by $r$ is the intersection of all the maximal finite subgroups of $W$ that contain it, then any isomorphism from $W$ to a Coxeter group $W'$ must take $r$ to a reflection in $W'$. The aim of this paper is to show how to determine, by inspection of the Coxeter graph, the intersection of the maximal finite sugroups containing $r$. In particular we show that the condition above is satisfied whenever $W$ is infinite and irreducible, and has the property that all rank two parabolic subgroups are finite. So in this case all isomorphisms map reflections to reflections.Comment: 25 pages, 0 figure

On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page

Local Government Revenue Mobilisation in Anglophone Africa

This paper examines opportunities and constraints facing local revenue mobilisation in anglophone Africa, with an emphasis on urban settings. It discusses specific revenue instruments and their effects on economic efficiency, income distribution and accountability. In particular, it addresses political and administrative constraints facing various revenue instruments and factors affecting citizens’ compliance. The analysis is illustrated with examples from across anglophone Africa. A general conclusion emerging from the study is that local revenues mobilised in most local government authorities in Africa are necessary but not sufficient to develop and supply adequate services for the fast-growing population. On this basis, areas for further research on local government revenue mobilisation in Africa are identifiedDfI

Should Market Value Be Retained as the Only Tax Base for Municipal Property Rates in South Africa?

In terms of the Local Government: Municipal Property Rates Act 6 of 2004 (MPRA), metropolitan and local municipalities in South Africa may levy property rates on property. The MPRA provides for only one tax base, namely "market value". Given the paucity of skills and capacity to prepare credible valuation rolls and given the costs of doing so, especially B3 and B4 local municipalities situated in rural areas are struggling to comply with the valuation-related provisions of the MPRA. A brief review of property tax base options utilised globally indicates that some countries allow for different tax bases (or even different taxes) on the basis of the location and/or use of property and some jurisdictions apply simplified methodologies (such as value banding, points-based assessment or even self-assessment) to assess properties for property tax purposes. In the light of there being viable alternatives to market value and of the challenges faced by many rural local municipalities, the South African government should revisit the policy decision to have only market value as the tax base across vastly different types of municipalities

n Regskritiese ondersoek na hereregte in Suid-Afrika

Proefskrif (LL. D.) -- Universiteit van Stellenbosch, 1990.Een kopie mikrofiche.Full text to be digitised and attached to bibliographic record

Property tax in Malaysia and South Africa: a question of assessment capacity and quality assurance

Many developing countries have been strengthening subnational government through decentralisation policies (Shah 2004). The supporting argument is based on the increased efficiency and welfare gains that come from moving governance closer to the people (Bahl 2009). Fiscal decentralisation can increase revenue mobilisation because it involves subnational government more directly in taxation, and, in many respects, a lower tier of government can reach wealth-based taxes in ways that central government cannot. The broadening of the local tax base, particularly with property taxes, gives subnational government a potentially lucrative revenue source (Cornia 2013; Kitchen 2013; Walters 2013). In terms of revenue mobilisation, the tax bases that are efficient and simple to administer at a subnational level tend to be few (Bird and Slack 2008; Mikesell 2013). Non-tax revenues (including user charges, licences, rents, and fees) tend to be limited in scope and revenuegenerating capacity. Local tax bases, according to Bird and Slack (2003), are narrow due to the possibility of tax exportation, externalities in the provision of public goods and services, factor mobility, and economies of scale. Broad tax bases, such as personal income tax, corporate income tax, and value-added tax (VAT), are generally best managed at higher levels of government. As a result, if subnational governments are to be important providers of public goods and services, it is necessary for higher level jurisdictions to share part of their revenues with subnational governments through transfers and grants to bridge the gap between spending and revenues mobilised locally (Bahl and Cyan 2010)