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Proceedings of the American Mathematical Society

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



Permutation groups with projective unitary subconstituents

Author: Richard Weiss
Journal: Proc. Amer. Math. Soc. 78 (1980), 157-161
MSC: Primary 20B15; Secondary 05C25
MathSciNet review: 550484
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Abstract: Let $ \Gamma $ be a finite directed graph with vertex set $ V(\Gamma )$ and edge set $ E(\Gamma )$ and let G be a subgroup of $ {\operatorname{aut}}(\Gamma )$ which we assume to act transitively on both $ V(\Gamma )$ and $ E(\Gamma )$. Suppose that for some prime power q, the stabilizer $ G(x)$ of a vertex x induces on both $ \{ y\vert(x,y) \in E(\Gamma )\} $ and $ \{ w\vert(w,x) \in E(\Gamma )\} $ a group lying between $ PSU(3,{q^2})$ and $ P\Gamma U(3,{q^2})$. It is shown that if G acts primitively on $ V(\Gamma )$, then for each edge (x, y), the subgroup of $ G(x)$ fixing every vertex in $ \{ w\vert(x,w)$ or $ (y,w) \in E(\Gamma )\} $ is trivial.

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Keywords: Primitive permutation group, subconstituent, projective unitary group, symmetric graph
Article copyright: © Copyright 1980 American Mathematical Society