In this paper, we investigate whether the stellar initial mass function (IMF) of early-type galaxies depends on their host environment. To this purpose, we have selected a sample of early-type galaxies from the SPIDER catalogue, characterized their environment through the group catalogue of Wang et al., and used their optical Sloan Digital Sky Survey (SDSS) spectra to constrain the IMF slope, through the analysis of IMF-sensitive spectral indices. To reach a high enough signal-to-noise ratio, we have stacked spectra in velocity dispersion (σ0) bins, on top of separating the sample by galaxy hierarchy and host halo mass, as proxies for galaxy environment. In order to constrain the IMF, we have compared observed line strengths and predictions of MIUSCAT/EMILES synthetic stellar population models, with varying age, metallicity, and `bimodal' (low-mass tapered) IMF slope (Γ _b). Consistent with previous studies, we find that Γ _b increases with σ0, becoming bottom-heavy (i.e. an excess of low-mass stars with respect to the Milky Way like IMF) at high σ0. We find that this result is robust against the set of isochrones used in the stellar population models, as well as the way the effect of elemental abundance ratios is taken into account. We thus conclude that it is possible to use currently state-of-the-art stellar population models and intermediate resolution spectra to consistently probe IMF variations. For the first time, we show that there is no dependence of Γb on environment or galaxy hierarchy, as measured within the 3 arcsec SDSS fibre, thus leaving the IMF as an intrinsic galaxy property, possibly set already at high redshift.