Solvable Hypergroups and a Generalization of Hall's Theorems on Finite Solvable Groups to Association Schemes

TL;DR

This paper extends Hall's theorems from finite solvable groups to the broader context of association schemes, using hypergroup theory as a foundational tool.

Contribution

It introduces a generalization of classical group theorems to association schemes, expanding the applicability of solvability concepts.

Findings

Generalization of Hall's theorems to association schemes

Development of hypergroup-based methods for scheme theory

New insights into the structure of solvable hypergroups

Abstract

We generalize Philip Hall's celebrated theorems on finite solvable groups to scheme theory. Our result is based on a series of results on hypergroups.