The Nyquist sampling theorem states that:

The sampling frequency Fs (aka sampling rate) for one continuous signal which has the maximum frequency of B shall be at least 2 B to avoid aliasing (i.e. perfect reconstruction).

The implies two facts:

1. If the maximum signal frequency B is known and we need to preserve the original signal, we must use a sampling frequency at least 2 B.
2. If the sampling frequency Fs is decided, we must limit the input signal's maximum frequency to Fs / 2 to avoid alasing, which can be conducted by pre-filtering input singal prior to sampling.

Now, if we want to further sub-sample the existing digital signal by a ratio 1 to N, the new sampling frequency becomes Fs / N. In order to avoid aliasing, the digital signal needs be pre-filtered to (Fs / N) / 2.