On p-schemes of order p3

JOURNAL OF ALGEBRA

卷:369

Article

Cho, Jung Rae¹  Hirasaka, Mitsugu¹  Kim, Kijung¹ 

[1] Pusan Natl Univ, Coll Nat Sci, Dept Math, Pusan 609735, South Korea

关键词: Association scheme;    p-Scheme;    Partial linear space;   

DOI  :  10.1016/j.jalgebra.2012.06.026

来源: Elsevier

【 摘 要 】

Let (X, S) be a p-scheme of order p(3) and T the thin residue of S. Assuming that T has valency p(2), one of the following holds: (i) vertical bar T vertical bar = p(2) and T similar or equal to C-p2; (ii) vertical bar T vertical bar = p(2) and T similar or equal to C-p x C-p : (iii) vertical bar T vertical bar < p(2). It is known that (X, S) is Schurian if (i) holds. In case (ii) we define a partial linear space on X/T and prove that the sizes of its lines coincide with the character degrees of (X, S). In case (iii) we give a construction of non-Schurian p-schemes which are algebraically isomorphic to a Schurian p-scheme of order p(3). (c) 2012 Elsevier Inc. All rights reserved.

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