In the immediate sunspots’ vicinity—their superpenumbra—3-minute line-of-sight (LOS) velocity oscillations dominate in the photosphere and chromosphere. Oscillations of similar periods are also registered in the transition region and lower corona above active regions. This work aims to clarify whether these LOS velocity oscillations are manifestations of Alfvénic waves in the lower solar atmosphere. The study is based on the analysis of three sunspots using data from instruments on board the Solar Dynamics Observatory. Additional observations of another sunspot were carried out at the ground-based Automated Solar Telescope. We use narrow-band frequency filtration (5.6 – 5.8 mHz) of the LOS velocity, magnetic field, and intensity signals of the Fe i 6173 Å spectral line. For the analysis, we use a 90-minute long time series. We conclude that the 3-minute oscillations in the LOS velocity signals result from magnetoacoustic waves rather than Alfvénic waves. However, oscillations registered in magnetic field signals indicate that Alfvénic waves may be present already in the photosphere. Further research requires simultaneous observations of LOS velocity, magnetic field strength, spectral line width, and intensity carried out at two heights of the solar atmosphere.