Mathematical Sciences: Asymptotic Properties of Finite Groups and Their Actions

古德曼96-23136 该补助金支持研究教授古德曼工作的问题在渐近行为置换行动有限群。例如，他希望确定渐近公式的大小可解子群的有限群G的数量方面的点上，该组可以忠实和传递。他还希望确定一个渐近公式的数量阿贝尔子群需要产生一个组。 这是一项跨越群论和组合学界限的研究。这些领域可以被认为是对抽象对称性的研究。因此，这一领域直接应用于物理和化学的许多领域。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。也有直接联系的纠错码是至关重要的现代计算，如与光盘的工作，以及理论计算机科学的一般。

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.