Mathematical Sciences: Asymptotic Properties of Finite Groups and Their Actions

本基金资助A Goodman教授研究有限群上置换作用的渐近行为问题。例如，他希望确定一个有限群G的可解子群的大小的渐近公式，根据该群可以忠实地和传递地作用的点的数目。他还希望确定生成一个群所需的阿贝尔子群数量的渐近公式。这项研究跨越了群论和组合学的界限。这些领域可以被认为是对抽象对称的研究。因此，这个领域对物理和化学的许多领域都有直接的应用。此外，在过去的30年里，许多与数据传输问题有关的问题已经用群论和组合学的技术解决了。它还与纠错码有直接的联系，纠错码对现代计算至关重要，比如使用CD-ROM以及一般的理论计算机科学。

Goodman 96-23136 This grant supports the research of Professor A Goodman to work on problems in the asymptotic behavior of permutation actions on finite groups. For example he hopes to determine asymptotic formulas for the size of solvable subgroups of a finite group G in terms of the number of points on which the group can act faithfully and transitively. He also hopes to determine an asymptotic formula for the number of abelian subgroups needed to generate a group. This is research that crosses the boundary between group theory and combinatorics. These areas can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory and combinatorics. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's as well as to theoretical computer science in general.