Unsolved Problems in Group Theory. The Kourovka Notebook

This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965. This is the 19th edition, which contains 111 new problems and a number of comments on about 1000 problems from the previous editions.Comment: A few new solutions and references have been added or update

Multicoloured Random Graphs: Constructions and Symmetry

This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will appear in physic

Maximal cocliques and cohomology in rank one linear groups

In this thesis, we investigate certain aspects of $\mathrm{PSL}_2(q)$. We begin by looking at the generating graph of $\mathrm{PSL}_2(q)$, a structure which may be used to encode certain information about the group, which was first introduced by Liebeck and Shalev and further investigated by many others. We provide a classification of maximal cocliques (independent sets) in the generating graph of $\mathrm{PSL}_2(q)$ when $q$ is a prime and provide a family of examples to show that this result does not directly extend to the prime-power case. After this, we instead investigate the cohomology of finite groups and prove a general result relating the first cohomology of any module to the structure of some fixed module and a generalisation of this result to higher cohomology. We then completely determine the cohomology $\mathrm{H}^n(G,V)$ and its generalisation, $\mathrm{Ext}_G^n(V,W)$, for irreducible modules $V$, $W$ for $G = \mathrm{PSL}_2(q)$ for all $q$ in all non-defining characteristics before doing the same for the Suzuki groups

Factors Influencing Customer Satisfaction towards E-shopping in Malaysia

Online shopping or e-shopping has changed the world of business and quite a few people have decided to work with these features. What their primary concerns precisely and the responses from the globalisation are the competency of incorporation while doing their businesses. E-shopping has also increased substantially in Malaysia in recent years. The rapid increase in the e-commerce industry in Malaysia has created the demand to emphasize on how to increase customer satisfaction while operating in the e-retailing environment. It is very important that customers are satisfied with the website, or else, they would not return. Therefore, a crucial fact to look into is that companies must ensure that their customers are satisfied with their purchases that are really essential from the ecommerce’s point of view. With is in mind, this study aimed at investigating customer satisfaction towards e-shopping in Malaysia. A total of 400 questionnaires were distributed among students randomly selected from various public and private universities located within Klang valley area. Total 369 questionnaires were returned, out of which 341 questionnaires were found usable for further analysis. Finally, SEM was employed to test the hypotheses. This study found that customer satisfaction towards e-shopping in Malaysia is to a great extent influenced by ease of use, trust, design of the website, online security and e-service quality. Finally, recommendations and future study direction is provided. Keywords: E-shopping, Customer satisfaction, Trust, Online security, E-service quality, Malaysia