Constraints on the duty cycle of the remnant radio galaxy NGC 6086 in the galaxy group Abell 2162

Galaxy clusters and groups are the most massive bounded structures and the knots of the large-scale structure of the Universe. These structures reside in dark matter haloes, hosting tens to hundreds of galaxies and they are filled with hot and rarefied gas. Radio Galaxies are a peculiar class of galaxies with a luminosity in the radio band up to 10^46 erg/s between 10 MHz and 100 GHz. These galaxies are a subclass of AGN in which there is accretion on the Super Massive Black Hole. The accretion generates jets of relativistic particles and magnetic fields which lose energy through synchrotron radiation, best observable at radio frequencies. The study of the spectral ageing of the AGN plasma is fundamental to understand its evolution, interaction with the environment and to constrain the AGN duty cycle. n this thesis, we have investigated the duty cycle of the nearby remnant radio galaxy NGC 6086, located in the centre of the galaxy group Abell 2162. We have made major steps forward thanks to the new high-sensitivity interferometers in the low-frequency radio band. We have detected for the first time three filaments of emission and a second couple of lobes. We have performed an integrated and resolved analysis on the previously known inner lobes, the new filaments and the older outer lobes. We have performed an age estimate of the two pairs of lobes to give constraints on the duty cycle of the source and an estimate of its active time.