Rank three innately transitive permutation groups and related $2$-transitive groupsThe sets of primitive, quasiprimitive, and innately transitive permutation
groups may each be regarded as the building blocks of finite transitive
permutation groups, and are analogues of composition factors for abstract
finite groups. This paper extends classifications of finite primitive and
quasiprimitive groups of rank at most $3$ to a classification for the finite
innately transitive groups. The new examples comprise three infinite families
and three sporadic examples. A necessary step in this classification was the
determination of certain configurations in finite almost simple $2$-transitive
groups called special pairs.
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