TY - JOUR

T1 - Solvable hypergroups and a generalization of Hall's theorems on finite solvable groups to association schemes

AU - Vasil'ev, Andrey V.

AU - Zieschang, Paul Hermann

N1 - Funding Information: The work of the first author was supported by the Ministry of Science and Higher Education of the Russian Federation [grant number 075-15-2019-1613 ]. Both authors would like to thank an anonymous referee for insightful comments on the first submission of this article. Publisher Copyright: © 2021 Elsevier Inc.

PY - 2022/3/15

Y1 - 2022/3/15

N2 - Within the class of hypergroups (in the sense of [8]) 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.

AB - Within the class of hypergroups (in the sense of [8]) 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.

KW - Association scheme

KW - Group theory and generalizations

KW - Hall's theorem

KW - Hypergroup

UR - http://www.scopus.com/inward/record.url?scp=85121640108&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.11.026

DO - 10.1016/j.jalgebra.2021.11.026

M3 - Article

AN - SCOPUS:85121640108

VL - 594

SP - 733

EP - 750

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -