  We prove that it is consistent with ZFC that no sequential topological groups
of intermediate sequential orders exist. This shows that the answer to a 1981
question of P.~Nyikos is independent of the standard axioms of set theory. The
model constructed also provides consistent answers to several questions of
D.~Shakhmatov, S.~Todor\v{c}evi\'c and Uzc\'ategui. In particular, we show that
it is consistent with ZFC that every countably compact sequential group is
Fr\'echet-Urysohn.
