A characterization and another construction of Janko’s group 𝐽₃

Weiss, Richard

doi:10.1090/S0002-9947-1986-0860383-2

A characterization and another construction of Janko’s group $J_ 3$
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Trans. Amer. Math. Soc. 298 (1986), 621-633 Request permission

Abstract:

Graphs $\Gamma$ with the following properties are classified: (i) $\Gamma$ is $(G,s)$-transitive for some $s \geqslant 4$ and some group $G \leqslant \operatorname {aut} (\Gamma )$ such that each vertex stabilizer in $G$ is finite, (ii) $s \geqslant (g - 1)/2$, where $g$ is the girth of $\Gamma$, and (ii) $\Gamma$ is connected. A new construction of ${J_3}$ is given.

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