Abstract: The concept of a hypergroup, dating back to the work of F. Marti in 1934, generalizes not only the concept of a group, but also an association scheme and table algebra. Within the class of hypergroups, we consider a specific class of hypergroups the members of which we call solvable. Our definition of solvable hypergroups generalizes the notion of a solvable group. We investigate solvable hypergroups and utilize our results to generalize Philip Hall's celebrated theorems on finite solvable groups to the theory of association schemes. The talk is based on the joint paper with P.-H. Zieschang.

Cite: Vasilev A.
Hypergroups, association schemes and Hall's theorems on finite solvable groups
In compilation The 5th International Conference «Groups and quandles in low-dimensional topology»: Program and abstracts. – Tomsk State University., 2024. – C.10.

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