Abstract
The Coxeter groups
are significantly useful because they are symmetric groups of the map
which is constructed from the tessellation
of the hyperbolic plane. It is now known that
is a factor group of the Coxeter groups
if
is a quadratic residue in the Galois field
, where
is a prime power. In this paper, we study Coxeter group
. By using a diagrammatic argument, propounded by G. Higman (2), we show that all but finitely many
and
, where
is congruent to
or 11 mod 20, are factor groups of
.