Commutativity of association schemes of prime square order having non-trivial thin closed subsets

Hanaki, Akihide1, Hirasaka, Mitsugu2, Uno, Katsuhiro3
1Faculty of Science, Shinshu University, Matsumoto, Japan
2Department of Mathematics College of Science, Pusan National University Kumjung, Pusan, Republic of Korea
3Department of Mathematical Sciences, Osaka Kyoiku University, Osaka, Japan

Tóm tắt

Through a study of the structure of the modular adjacency algebra over a field of positive characteristic p for a scheme of prime order p and utilizing the fact that every scheme of prime order is commutative, we show that every association scheme of prime square order having a non-trivial thin closed subset is commutative.

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citation_title=Algebraic Combinatorics I; citation_publication_date=1984; citation_id=CR1; citation_author=E. Bannai; citation_author=T. Ito; citation_publisher=Benjamin/Cummings citation_title=Methods of Representation Theory, vol. I; citation_publication_date=1981; citation_id=CR2; citation_author=C.W. Curtis; citation_author=I. Reiner; citation_publisher=Wiley citation_journal_title=J. Algebr. Comb.; citation_title=Transitive permutation groups of prime-squared degree; citation_author=E. Dobson, D. Witte; citation_volume=16; citation_issue=1; citation_publication_date=2002; citation_pages=43-69; citation_doi=10.1023/A:1020882414534; citation_id=CR3 citation_journal_title=Arch. Math. (Basel); citation_title=Locality of a modular adjacency algebra of an association scheme of prime power order; citation_author=A. Hanaki; citation_volume=79; citation_issue=3; citation_publication_date=2002; citation_pages=167-170; citation_id=CR4 citation_journal_title=Graphs Comb.; citation_title=Representations of association schemes and their factor schemes; citation_author=A. Hanaki; citation_volume=19; citation_issue=2; citation_publication_date=2003; citation_pages=195-201; citation_id=CR5 citation_journal_title=Proc. Am. Math. Soc.; citation_title=Characters of association schemes containing a strongly normal closed subset of prime index; citation_author=A. Hanaki; citation_volume=135; citation_issue=9; citation_publication_date=2007; citation_pages=2683-2687; citation_doi=10.1090/S0002-9939-07-08835-1; citation_id=CR6 citation_journal_title=J. Algebr. Comb.; citation_title=Algebraic structure of association schemes of prime order; citation_author=A. Hanaki, K. Uno; citation_volume=23; citation_issue=2; citation_publication_date=2006; citation_pages=189-195; citation_doi=10.1007/s10801-006-6923-7; citation_id=CR7 citation_title=Elementary and Analytic Theory of Algebraic Numbers; citation_publication_date=2004; citation_id=CR8; citation_author=W. Narkiewicz; citation_publisher=Springer citation_title=Theory of Association Schemes; citation_publication_date=2005; citation_id=CR9; citation_author=P.-H. Zieschang; citation_publisher=Springer