The \(\pi \)-radical and Hall's theorems for residually thin and \(\pi \)-valenced hypergroups, table algebras, and association schemes

DOI10.1016/j.jalgebra.2022.03.001OpenAlexW4220677378WikidataQ115193787 ScholiaQ115193787MaRDI QIDQ2118944

Harvey I. Blau

Publication date: 23 March 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2022.03.001

zbMATH Keywords

association schemehypergrouptable algebraHall theorems\(\pi\)-radicalresidually thin

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Association schemes, strongly regular graphs (05E30) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Hypergroups (20N20)

Cites Work

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• Table algebras
• The theory of finite groups. An introduction.
• Sylow theory for table algebras, fusion rule algebras, and hypergroups.
• Generalized table algebras
• Solvable hypergroups and a generalization of Hall's theorems on finite solvable groups to association schemes
• On residually thin hypergroups
• On a class of wreath products of hypergroups and association schemes.
• Solvability of groups of odd order

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