The Sylow theorems and their generalizations

Thesis (M.A.)--Boston UniversityThe thesis treats the generalization of Sylow's theorems about p-subgroups to theorems concerning Hall π-subgroups. The Hall π-subgroup is an extension of the Sylow p-subgroup to a set of primes π instead of the single prime p. ln the first section Sylow's theorems are stated and the Hall π-subgroup is defined. Hall [3] generalized Sylow's theorems completely in the case of solvable groups. ln particular he showed that every solvable group possesses a Hall π-subgroup for any set of primes. He also showed [4] that if a group G is not solvable there is at least one set of primes π such that G possesses no Hall π-subgroup. His results are discussed in section 2 and some examples of insolvable groups for which his generalized theorems are invalid are given. For a particular set of primes π it is possible to generalize Sylow's theorems even when the groups being considered are not necessarily solvable. Some theorems of this type are considered in section 3. For example, one of the theorems gives sufficient conditions, depending on the set of primes π, a group to possess a Hall π-subgroup. For a particular set of primes π, solvability can be generalized to π-separability and π-solvability. Theorems similar to Hall's theorems for solvable groups can be proved for π-separable and π-solvable groups. These are discussed in section 4. A theorem concerning sufficient conditions for a group to be π-separable is proved. Finally in section 5, some of the results of the earlier sections are applied to the problem of subnormal subgroups and their normalizers

Keep Tinkering: The Optimist and the Death Penalty

When it comes to capital punishment, it may make sense to be a little bit defeatist. Like abortion, the death penalty is a topic about which you have to presume that you are never going to change anyone else’s mind. Whether the other person views it as a necessary part of the justice system or as a moral outrage, odds of changing the other person’s mind through reasoned discourse are slim

POVERTY AND ACCESS TO INFRASTRUCTURE IN PAPUA NEW GUINEA

In this paper, our overall goal is to understand how effective access to infrastructure is in reducing poverty in PNG. To meet this goal, we examine poverty in PNG, and seek to show the relationship between poverty and access to infrastructure and then identify the determinants of poverty. In our analysis, we test whether or not access to infrastructure is a significant factor in a household's poverty status. Finally, we want to understand what policies will be effective in overcoming poverty in PNG. Our results show that poverty in PNG is primarily rural and is associated with those in communities with poor access to services, markets, and transportation. Our simulations illustrate that improving access to school leads to large declines in poverty. Increasing access to poverty for those that are currently most isolated would have a significant effect in decreasing the severity of poverty.Food Security and Poverty, Public Economics,

Transition, development and the supply of wheat in China

The overall goal of this article is to better understand the factors that influence China’s wheat supply. We assess trends in China’s wheat output and develop a framework to measure the relationship between output and key determinants of China’s wheat sector growth. Elasticity estimates and factor growth trends help decompose the growth of reform‐era wheat supply into its component parts. The results show that growth in the early reform period was due to institutional change and technology. In the late reform period, however, with the returns to institutional change exhausted, all of China’s growth in wheat supply was due to technology, a result that implies China’s government should invest heavily in agricultural research and development.Crop Production/Industries,

IS IT BETTER TO BE A BOY? A DISAGGREGATED OUTLAY EQUIVALENT ANALYSIS OF GENDER BIAS IN PAPUA NEW GUINEA

Discrimination in the allocation of goods between boys and girls within households in Papua New Guinea is examined using Deatons (1989) outlay-equivalent ratio method. Adding a boy to the household reduces expenditure on adult goods by as much as would a nine-tenths reduction in total outlay per member, but girls have no effect on adult goods expenditure. The hypothesis of Haddad and Reardon (1993) that gender bias is inversely related to the importance of female labour in agricultural production is not supported. There is no evidence of bias against girls in the urban sector.Labor and Human Capital,

CHINA'S ACCESSION TO WTO AND SHIFTS IN THE AGRICULTURE POLICY

The overall goal of our paper is to explore this question of how China's policy will likely respond as the nation enters the WTO. Specifically, we will have three objectives. First, we briefly review China's existing agriculture policy and past performance of China's agriculture and how it has changed during the past 20 years of reform. Next, we examine the main features of the agreement that China must adhere to as they enter WTO. Finally, we consider a number of possible ways that policy makers may respond, primarily focusing on the national government's viewpoint.International Relations/Trade,

Market development and food demand in rural China

This paper seeks to understand how market imperfections affect the behavior of consumers in China's rural economy. A theoretical and empirical model is developed and estimated using a household-level data from six counties in Hebei Province. The results show that market development plays an important role in explaining food consumption behavior in China. As the market develops, farmers demand less grain and vegetables and consume more meat, fruit, and other food products after control for income and price effects. Moreover, the elasticities of demand also change as farm households begin to rely more on rural markets. The results of this paper suggest that a government concerned about the welfare of its rural population may want to be paying a more active role in fostering rural markets. Understanding the forces behind these consumption pattern shifts also will aid academics and policymakers in making better projections about future consumerneeds and price levels.Prices Government policy. ,Food consumption. ,Rural population. ,

How widespread are non-linear crowding out effects? The response of private transfers to income in four developing countries

This paper investigates whether there is a non-linear relationship between income and the private transfers received by households in developing countries. If private transfers are unresponsive to household income, expansion of public social security and other transfer programs is unlikely to crowd out private transfers, contrary to concerns first raised by Barro and Becker. There is little existing evidence for crowding out effects in the literature, but this may be because they have been obscured by methods that ignore non-linearities. If donors switch from altruistic motivations to exchange motivations as recipient income increases, a sharp non-linear relationship between private transfers and income may result. In fact, threshold regression techniques find such non-linearity in the Philippines and after accounting for these there is evidence of serious crowding out, with 30 to 80 percent of private transfers potentially displaced for low-income households [Cox, Hansen and Jimenez 2004, 'How Responsiveare Private Transfers to Income?' Journal of Public Economics]. To see if these non-linear effects occur more widely, semiparametric and threshold regression methods are used to model private transfers in four developing countries - China, Indonesia, Papua New Guinea and Vietnam. The results of our paper suggest that non-linear crowding-out effects are not important features of transfer behaviour in these countries. The transfer derivatives under a variety of assumptions only range between 0 and -0.08. If our results are valid, expansions of public social security to cover the poorest households need not be stymied by offsetting private responses