 Rank of a transitive permutation group (source code)

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= Rank of a transitive permutation group
{title2=$\operatorname{rank}(G)=|G_\alpha\backslash\Omega|$}

= Permutation rank
{synonym}

The number of point-stabilizer orbits, equivalently the number of orbits on ordered pairs. On $k$-spaces of an $n$-space with $k\le n/2$, $GL_n(q)$ has rank $k+1$, indexed by intersection dimension.

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