## Permutation groups with projective unitary subconstituents

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- by Richard Weiss PDF
- Proc. Amer. Math. Soc.
**78**(1980), 157-161 Request permission

## 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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## Additional Information

- © Copyright 1980 American Mathematical Society
- 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