# Invariant Relations and Aschbacher Classes of Finite Linear Groups

@article{Xu2011InvariantRA, title={Invariant Relations and Aschbacher Classes of Finite Linear Groups}, author={Jing Xu and Michael Giudici and Cai Heng Li and Cheryl E. Praeger}, journal={Electr. J. Comb.}, year={2011}, volume={18} }

For a positive integer $k$, a $k$-relation on a set $\Omega$ is a non-empty subset $\Delta$ of the $k$-fold Cartesian product $\Omega^k$; $\Delta$ is called a $k$-relation for a permutation group $H$ on $\Omega$ if $H$ leaves $\Delta$ invariant setwise. The $k$-closure $H^{(k)}$ of $H$, in the sense of Wielandt, is the largest permutation group $K$ on $\Omega$ such that the set of $k$-relations for $K$ is equal to the set of $k$-relations for $H$. We study $k$-relations for finite semi-linear… CONTINUE READING

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