Abstract
Let p denote a prime number. In this note, we focus on the modular Terwilliger algebras of association schemes defined in Hanaki (Graphs Combin, 2021, https://doi.org/10.1007/s00373-021-02363-0). We define the primary module of a modular Terwilliger algebra of an association scheme and determine all its composition factors up to isomorphism. We then characterize the \(p'\)-valenced association schemes in terms of numerous properties of their modular Terwilliger algebras. We conclude our investigation with a few corollaries and questions on the modular Terwilliger algebras of association schemes.
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