On some p-transitive association schemes. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Jiang, Yu
• Is Part Of: Communications in algebra. Volume 50:Issue 3(2022)
• Page Start: 1169
• Page End: 1181
• Publication Date: 2022-03-04
• Subjects: Association scheme -- quasi-thin scheme -- scheme with thin thin residue; 05E30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1979027
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this paper, for any prime p, we propose the notion of a p -transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique principal submodule to the case of the regular modules of modular adjacency algebras of association schemes. We characterize the p -transitive quasi-thin association schemes and the p -transitive association schemes with thin thin residue by their structure theory properties. We also get some results with independent interests.