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