# Semi-group in quantum open systems

In the literature of Open Quantum System, one often comes across the following ($$t_2>t_1,>0$$):

Semi-group property of a map: $$A(t_1+t_2,0) = A(t_2,0) A(t_1,0)$$.

What does this mean physically, and why the name semi-group?

$$\frac{dp_t}{dt}=Lp_t$$
$$A_t=e^{tL}$$
$$A_{t+s}=A_tA_s$$