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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A characterization and another construction of Janko's group $ J\sb 3$


Author: Richard Weiss
Journal: Trans. Amer. Math. Soc. 298 (1986), 621-633
MSC: Primary 20D08; Secondary 05C25, 20F05
DOI: https://doi.org/10.1090/S0002-9947-1986-0860383-2
MathSciNet review: 860383
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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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DOI: https://doi.org/10.1090/S0002-9947-1986-0860383-2
Article copyright: © Copyright 1986 American Mathematical Society