Transversals in Groups with an application to loops

这个项目的目的是研究群G中子群的截线。我们计划研究两种类型的问题：(a)假设G的一个子群，或G的每一个子群或G的一个特殊的子群类存在某种类型的截线——例如正规或全局截线。这对G的结构有什么影响？(b)设G是某种类型的群——例如原群、超溶群或可溶群——哪一种类型的截线必须存在？特别地，我们计划继续对问题(a)的一种特殊情况——简单Bol环的分类，以及对具有正则子群的原始置换群的分类。

The aim of the project is to study transversals of subgroups in a group G. We plan to investigate two types of questions: (a) Suppose a certain type of transversal exists - for instance a normal or global transversal - for a subgroup of G, or for each subgroup of G or a special class of subgroups of G. What is the implication of this on the structure of G?(b) Let G be a certain type of group - for instance primitive, supersoluble or soluble - which type of transversal has to exist?In particular, we plan to continue the classification of the simple Bol loops, which is a special case of question (a), as well as the classification of the primitive permutation groups which possess a regular subgroup.