  Together with their 1988 construction of the monster vertex algebra
$V^\natural$, Frenkel, Lepowsky, and Meurman showed that the largest sporadic
simple group, known as the Fischer-Griess monster, forms the symmetry group of
an infinite dimensional algebraic object whose construction was motivated by
theoretical physics. However, the fact that the symmetry group is in fact
finite and simple ultimately relied on highly non-trivial group-theoretic
results used in Griess's work on the monster. We prove some properties of the
automorphism group of $V^\natural$, most notably that it is is finite and
simple, using recent developments in the theory of vertex operator algebras,
but mostly 19th century group theory.
