Finite index subgroups of R. Thompson's group F

Details Finite index subgroups of R. Thompson's group F Finite index subgroups of R. Thompson's group F

2007-11-07

arxiv.org/abs/0711.1014v1

Mathematics

Group Theory

26 pages, 8 figures

Scientific paper

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 properties of the structure of the finite index subgroups of $Z\times Z$.

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