On association schemes with thin thin residue. (English) Zbl 1213.05267
Summary: Let \(S\) be a scheme of finite valency, and assume that \(O^\vartheta(S)\subseteq O_\vartheta(S)\). It is known that \(S\) is schurian (which means that \(S\) arises from a finite group) if the normal closed subsets (normal subgroups) of j\(O^\vartheta(S)\) are linearly ordered with respect to settheoretic inclusion; cf. [M. Hirasaka and P.-H. Zieschang, J. Comb. Theory, Ser. A 104, No. 1, 17–27 (2003; Zbl 1031.05136)]. In this note, it is shown that \(S\) is schurian if \(O^\vartheta(S)\) is direct product of two simple closed subsets (finite simple groups) of different order.
MSC:
| 05E30 | Association schemes, strongly regular graphs |
Citations:
Zbl 1031.05136References:
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