  We investigate locally compact topological groups for which a generalized
analogue of Heisenberg uncertainty inequality hold. In particular, it is shown
that this inequality holds for $\mathbb{R}^n \times K$ (where $K$ is a
separable unimodular locally compact group of type I), Euclidean Motion group
and several general classes of nilpotent Lie groups which include thread-like
nilpotent Lie groups, $2$-NPC nilpotent Lie groups and several low-dimensional
nilpotent Lie groups.
