Mathematical Sciences: Asymptotic Properties of Finite Groups and Their Actions

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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.