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On a generalization of the notion of group. (Sur une généralisation de la notion de groupe.) (French) Zbl 0012.05303

8. Skand. Mat.-Kongr., Stockholm 1934, 45-49 (1935).
A set with four operations, right and left products, right and left quotients, is a hypergroup if the multiplications are associative. The operations need not be unique. The author shows that uniqueness of one division implies uniqueness of the other and of multiplication. A completely regular hypergroup contains a unit and the inverse of every element. Multiplication of the sets of conjugates in a group is defined so that they form a completely regular hypergroup. The hypergroup of automorphism of a rational fraction belongs, in this sense, to the Galois group of an algebraic extension of the rational numbers.

MSC:

20N20 Hypergroups

Keywords:

hypergroup