Classification of involutive commutative two-valued groups

Abstract

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: a principal series, a unipotent series, and a special series; it is shown that any finitely generated involutive commutative two-valued group is isomorphic to a two-valued group in one of these series. A number of classification results are obtained for topological involutive commutative two-valued groups in the Hausdorff and locally compact cases. The classification of algebraic involutive two-valued groups in the one-dimensional case is also discussed. Bibliography: 45 titles.