Abstract:
This paper deals with the algebraic theory of multi-valued formal groups. The letters FG will be used to mean an $n$-valued formal group.
It is shown that to any FG there corresponds a coalgebra of a certain form. The form of the generator of an FG is obtained, and differential equations involving the coefficients of the generator are derived. It is shown that an FG can be uniquely reproduced by its generator. The generator of a cyclic elementary group is computed. A classification is obtained for the three-valued, four-valued, and five-valued FG's. It is proved that there exist finitely many elementary FG's with order not greater than 11.
Bibliography: 4 titles.
Fulltext:
PDF file (1751 kB)
