  Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a
maximal subfactor. We answer it affirmatively by three different approaches,
all containing the same key ingredient: the existence of maximal subgroups with
infinite index. We also show that point stabilizer subgroups for every
faithful, 4-transitive action on an infinite set give rise to maximal von
Neumann subalgebras. Combining this with known results on constructing
faithful, highly transitive actions, we get many maximal von Neumann
subalgebras arising from maximal subgroups with infinite index.

Operator Algebras;Group Theory