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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0550484-0
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 $\{ y|(x,y) \in E(\Gamma )\}$ and $\{ w|(w,x) \in E(\Gamma )\}$ 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 $\{ w|(x,w)$ 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