Characteristics quotients
of the
Universal p-Frattini cover of
a finite group
The analog depends on
knowing that there exists a natural sequence of covers with p
group
kernels of any finite group G with order divisible by p. The
key being
the first construction step in that sequence. The analogy works well if
G is p-perfect, where it produces spaces for which we can
formulate
conjectures on various ways they are similar to modular curves.