  If G and X are groups and N is a normal subgroup of X, then the G-closure of
N in X is the normal subgroup X^G= bigcap{kerphi|phi:X-> G, with N subseteq
kerphi} of X . In particular, 1^G = R_G X is the G-radical of X. Plotkin calls
two groups G and H geometrically equivalent, written G H, if for any free group
F of finite rank and any normal subgroup N of F the G-closure and the H-closure
of N in F are the same. Quasiidentities are formulas of the form
(bigwedge_{i<=n}w_i=1 -> w =1) for any words w, w_i (i<=n) in a free group.
Generally geometrically equivalent groups satisfy the same quasiidentiies.
Plotkin showed that nilpotent groups G and H satisfy the same quasiidenties if
and only if G and H are geometrically equivalent. Hence he conjectured that
this might hold for any pair of groups. We provide a counterexample.
