Semiautomorphic Inverse Property Loops

We define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied variety of loops. Next we extend several known results for Moufang and Steiner loops. That is, the commutant is a subloop and if $a$ is in the commutant, then $a^{2}$ is a Moufang element, $a^{3}$ is a $c$-element and $a^{6}$ is in the center. Finally, we give two constructions for semiautomorphic inverse property loops based on Chein's and de Barros and Juriaans' doubling constructions.Comment: Preprin

A class of loops categorically isomorphic to Bruck loops of odd order

We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of odd order and $\Gamma$-loops of odd order. Once this has been established, we can use the well known structure of Bruck loops of odd order to derive the Odd Order, Lagrange and Cauchy Theorems for $\Gamma$-loops of odd order, as well as the nontriviality of the center of finite $\Gamma$-$p$-loops ($p$ odd). Finally, we answer a question posed by Jedli\v{c}ka, Kinyon and Vojt\v{e}chovsk\'{y} about the existence of Hall $\pi$-subloops and Sylow $p$-subloops in commutative automorphic loops. By showing commutative automorphic loops are $\Gamma$-loops and using the categorical isomorphism, we answer in the affirmative

Loops and Their Permutation Groups

This dissertation uses the connections between loops and their associated permutation groups to study certain varieties of loops. We first define a variety of loops generalizing commutative automorphic loops and show this new variety is power associative. We show a correspondence to Bruck loops of odd order and use this correspondence to give structural results for our new variety, which in turn hold for commutative automorphic loops. Next, we study a variety of loops that generalize both Moufang and Steiner loops. We extend on known results for Moufang loops and then extend two different doubling constructions for creating Moufang and other varieties of loops. We then give a general construction to create simple RCC loops from GL(2,q) for q a prime power. Finally, we consider a generalization of Bruck loops, and show that different companions of pseudoautomorphism live in certain subloops

Imputation, Fairness and the Family Home

This commentary assesses the Court of Appeal ruling in Graham-York v York [2015] EWCA Civ 72 on whether a 25 per cent beneficial interest in the family home was a "fair reflection" of the claimant's contributions towards repaying the mortgage, the household expenses and raising the child of her 33-year cohabitation with her deceased partner. The writers' conclusion is that Graham-York represents a significant shift away from a holistic approach to quantification in single ownership cases. The range of relevant factors in quantifying the parties' respective beneficial shares should be deployed objectively without any obvious bias against contributions of a non-financial or purely domestic nature. Otherwise, the court is not dispensing justice to the parties

The role and development of life skills in young sports participants

Under the umbrella of positive youth development, life skills represent an important area of research for young people. The personal competencies a young person possesses determine his or her capacity to effectively navigate the turbulence of adolescence and grow into adulthood. An increased understanding of the role, function, and enhancement of life skills therefore serves a great purpose in the design and evaluation of youth development programs. This thesis aimed to extend the current knowledge and practices through targeting the gaps in the life skills literature. First, using a qualitative design, the specific needs of young elite athletes were investigated while outlining a proposed methodology for future needs analyses. The importance of developing life skills in young athletes was emphasised as it was found that young athletes required a range of both sport specific and life skills. Second, an investigation into the function of life skills found that reported possession of key life skills partially mediates the relationship between youth experiences and well-being, illustrating this role for the first time. However, within youth samples there was a broad range in the degree to which these skills are applied and transferred, reinforcing the call for deliberate developmental programming. The lack of adequate measures in life skills research was addressed through the validation of BRSQ with young sports participants. Support for the utility of this measure allows for the greater investigation into the mechanisms through which life skills function. Finally, a life skills program was designed following the recommendations of the predominant youth development frameworks and comprehensively evaluated. This thesis progresses existing literature regarding the role and function of life skills as well as providing insight into how to best promote and evaluate the teaching of life skills in applied research programs

Moufang semidirect products of loops with groups and inverse property extensions

We investigate Moufang loops which can be written as the semidirect product of a loop and a group. We also examine a particular class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. A question posed by Gagola III related to such extensions is partially answered, and we give several examples which illustrate that, in general, these extensions are not well-behaved.Comment: preprin

CONSTRUCTIVE TRUSTS AND THE HOMEMAKER

To what extent, following the decisions in Stack v Dowden and Abbott v Abbott, may a claimant acquire beneficial ownership in the family home under a constructive trust relying purely on domestic contributions as homemaker?  The writers examine this question against the background of single and joint ownership cases and suggest that, in the light of recent judicial pronouncements, the criteria for establishing a common intention constructive trust enunciated by Lord Bridge in Lloyds Bank plc v Rosset may have been eroded so as to allow for a much broader inquiry of the claimant’s contributions to support a constructive trust.  In particular, it is submitted that this may allow the English courts to consider the same factors for both establishing and quantifying the claimant’s interest in the property which, in turn, may pave the way for a closer assimilation between single and joint ownership cases in this field