Characters of finite quasigroups. VI: Critical examples and doubletons
[Part V see ibid. 10, No.5, 449-456 (1989; Zbl 0679.20059).] The aim of this paper is to present critical examples of scheme character tables which are demonstrably not quasigroup character tables. Immediate sporadic examples are offered by the character tables of the schemes given by strongly regular graphs with 26 vertices. The main task of the note is to present members of an infinite family of examples, such as \[ \left[\begin{matrix} 1 & 1 & 1 \\ \sqrt{7} & 1/3\sqrt{7} & -1/3\sqrt{7} \\ 2\sqrt{5} & -1/3\sqrt{5} & 2/15\sqrt{5}\end{matrix}\right] \] of scheme character tables which are demonstrably not quasigroup character tables. This is done in Theorem: Let r be an even integer greater than 4. Then the character table of the Johnson scheme \(J(r,2)\) is not a quasigroup character table.
scientific article; zbMATH DE number 4154750
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