Finite index subgroups of R. Thompson’s group F

The authors classify the finite index subgroups of R. Thompson’s group F. All such groups that are not isomorphic to F are non-split extensions of finite cyclic groups by F. The classification describes precisely which finite index subgroups of F are isomorphic to F, and also separates the isomorphism classes of the finite index subgroups of F which are not isomorphic to F from each other; characterizing the structure of the extensions using the structure of the finite index subgroups of Z × Z.