Classification of six-, seven-, and eight-valued elementary formal groups
In the paper in Izv. Akad. Nauk SSSR, Ser. Mat. 39, 1044-1064 (1975; Zbl 0324.14010); translation in Math. USSR, Izv. 9(1975), 987-1006 (1977), \textit{V. M. Bukhshtaber} introduced the concept of one-dimensional multiple-valued commutative formal groups (FG) and constructed an algebraic apparatus for investigating two-valued FG. Using these methods, the author [Mat. Sb., Nov. Ser. 114(156), 299-321 (1981; Zbl 0474.14029); translation in Math. USSR, Sb. 42, 265-285 (1982)] constructed an algebraic apparatus for investigating n-valued FG, for any natural number n, over \({\mathbb{Q}}\)-algebras, where \({\mathbb{Q}}\) is the field of rational numbers. As shown in the cited papers, in studying FG it is first necessary to investigate elementary FG (EFG). The paper cited first offered a classification of two-valued EFG, and the second one a classification of n-valued EFG whose order does not exceed 5, and it was shown that there exists a finite number of EFG whose order does not exceed 11. In this paper, we give a classification of six-, seven-, and eight-valued EFG. We note that the results are in agreement with the hypotheses regarding the structure of EFG that were advanced in the author's cited paper.
multiple-valued commutative formal groups
scientific article; zbMATH DE number 3966307