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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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