  Based on a recently introduced by the author notion of {\em parity}, in the
present paper we construct a sequence of invariants (indexed by natural numbers
$m$) of long virtual knots, valued in certain simply-defined group ${\tilde
G}_{m}$ (the Cayley graphs of these groups are represented by grids in the
$(m+1)$-space); the conjugacy classes of elements of $G_{m}$ play the role of
invariants of {\em compact} virtual knots. By construction, all invariants do
not change under {\em virtualization}. Factoring the group algebra of the
corresponding group by certain polynomial relations leads to finite order
invariants of (long) knots which do not change under {\em virtualization
