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A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let be a nontrivial finite regular linear space and Suppose that is extremely primitive on points and let rank be the rank of on points. We prove that rank with few exceptions. Moreover, we show that is neither a sporadic group nor an alternating group, and with a Fermat prime if is a finite classical simple group.
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