  After providing a short review on the recently introduced notion of
post-group by Bai, Guo, Sheng and Tang, we exhibit post-group counterparts of
important post-Lie algebras in the literature, including the
infinite-dimensional post-Lie algebra of Lie group integrators. The notion of
free post-group is examined, and a group isomorphism between the two group
structures associated to a free post-group is explicitly constructed.
