Commutativity of association schemes of prime square order having non-trivial thin closed subsets
Akihide Hanaki1
, Mitsugu Hirasaka2
and Katsuhiro Uno3
1Shinshu University Faculty of Science Matsumoto 390-8621 Japan
2Pusan National University Kumjung Department of Mathematics, College of Science Pusan 609-735 Republic of Korea
3Osaka Kyoiku University Department of Mathematical Sciences Kashiwara Osaka 582-8582 Japan
2Pusan National University Kumjung Department of Mathematics, College of Science Pusan 609-735 Republic of Korea
3Osaka Kyoiku University Department of Mathematical Sciences Kashiwara Osaka 582-8582 Japan
DOI: 10.1007/s10801-007-0090-3
Abstract
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.
Pages: 307–316
Keywords: keywords association scheme; closed subset; character
Full Text: PDF
References
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3. Dobson, E., Witte, D.: Transitive permutation groups of prime-squared degree. J. Algebr. Comb. 16(1), 43-69 (2002)
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2. Curtis, C.W., Reiner, I.: Methods of Representation Theory, vol. I. Wiley, New York (1981)
3. Dobson, E., Witte, D.: Transitive permutation groups of prime-squared degree. J. Algebr. Comb. 16(1), 43-69 (2002)
4. Hanaki, A.: Locality of a modular adjacency algebra of an association scheme of prime power order.