  We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat
equation on an arbitrary stratified Lie group with homogeneous dimension $Q$.
This covers the Euclidean case and gives new insight into proof techniques on
nilpotent Lie groups. The equation we study has a forcing term which depends
only upon a group element and has positive integral. The stratified Lie group
structure plays an important role in our proofs, along with test function
method and Banach fixed point theorem.
