  We present a series of examples of nondiscrete reflexive P-groups (i.e.,
groups in which all $G_\delta$-sets are open) as well as noncompact reflexive
$\omega$-bounded groups (in which the closure of every countable set is
compact). Our main result implies that every product of feathered
(equivalently, almost metrizable) Abelian groups equipped with the P-modified
topology is a reflexive group. In particular, every compact Abelian group with
the P-modified topology is reflexive. This answers a question posed by S.
Hern\'andez and P. Nickolas and solves a problem raised by Ardanza-Trevijano,
Chasco, Dom\'{\i}nguez, and Tkachenko.
