From: Walter Neumann 
Subject: Question about characteristic subgroups
Date: Mon, 24 Mar 1997 11:15:20 -0500 (EST)

Let $G_n$ be the surface group of genus $n$ (fundamental group of the
orientable closed surface of genus $n$). Consider the following
equivalence relation on the set of integers $n>1$: 
 
   $n$ is equivalent to $m$ if $G_n$ and $G_m$ have isomorphic
   characteristic subgroups of finite index.
 
Is anything known about the number of equivalence classes for this
relation?
 
--walter neumann