Maximal Schottky extension groups (Q976834)

The main result is a combinatorial description of Schottky extension groups; which are Kleinian groups \(K\) containing a Schottky group \(G\) (of rank \(g\) at least \(2\)) as a normal subgroup. The maximal index of \(G\) in \(K\) is known to be \(12(g-1)\), and if this bound is achieved, \(G\) is said to be \textit{maximal}. As a corollary of the main result, it is shown (reproving a result of Zimmerman) that any maximal Schottky extension group is (isomorphic to) one of a list of 4 possible groups.