  We report the discovery of active star formation in Digel's Cloud 2, which is
one of the most distant giant molecular clouds known in the extreme outer
Galaxy (EOG). At the probable Galactic radius of ~20 kpc, Cloud 2 has a quite
different environment from that in the solar neighborhood, including lower
metallicity, much lower gas density, and small or no perturbation from spiral
arms. With new wide-field near-infrared (NIR) imaging that covers the entire
Cloud 2, we discovered two young embedded star clusters located in the two
dense cores of the cloud. Using our NIR and 12CO data as well as HI, radio
continuum, and IRAS data in the archives, we discuss the detailed star
formation processes in this unique environment. We show clear evidences of a
sequential star formation triggered by the nearby huge supernova remnant, GSH
138-01-94. The two embedded clusters show a distinct morphology difference: the
one in the northern molecular cloud core is a loose association with
isolated-mode star formation, while the other in the southern molecular cloud
core is a dense cluster with cluster-mode star formation. We propose that high
compression by the combination of the SNR shell and an adjacent shell caused
the dense cluster formation in the southern core. Along with the low
metallicity range of the EOG, we suggest that EOG could be an excellent
laboratory for the study of star formation processes, such as those triggered
by supernovae, that occured during an early epoch of the Galaxy's formation. In
particular, the study of the EOG may shed light on the origin and role of the
thick disk, whose metallicity range matches with that of the EOG well.
