  V.I.Arnold has classified simple (i.e. having no modules for the
classification) singularities (function germs), and also simple boundary
singularities (function germs invariant with respect to the action $\sigma(x_1;
y_1, \ldots, y_n)=(-x_1; y_1, \ldots, y_n)$ of the group $Z_2$. In particular,
it was shown that a function germ (respectively a boundary singularity germ) is
simple if and only if the intersection form (respectively the restriction of
the intersection form to the subspace to anti-invariant cycles) of a germ in
$3+4s$ variables stable equivalent to the one under consideration is negative
definite and if and only if the (equivariant) monodromy group on the
corresponding subspace is finite. We formulate and prove analogues of these
statements for function germs invariant with respect to an arbitrary action of
the group $Z_2$ and also for corner singularities.
