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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The graph extension theorem


Author: Ernest Shult
Journal: Proc. Amer. Math. Soc. 33 (1972), 278-284
MSC: Primary 20B99
DOI: https://doi.org/10.1090/S0002-9939-1972-0294477-5
MathSciNet review: 0294477
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Abstract: A sufficient condition is given that a transitive permutation group G admits a transitive extension $ {G^\ast}$. The condition is graph-theoretic and does not involve any direct algebraic properties of the group being extended. The result accounts for a fairly wide class of doubly transitive groups, including the two doubly transitive representations of the groups $ {\text{Sp}}(2n,2)$, and the doubly transitive representations of the Higman-Sims group, and the Conway group (.3).


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294477-5
Keywords: Doubly transitive groups, transitive extension, automorphism groups of graphs
Article copyright: © Copyright 1972 American Mathematical Society

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