Probes of flavour symmetry and violation with top quarks in ATLAS and CMS

Results are presented of searches and measurements in the top quark sector by the ATLAS and CMS experiments. These analyses use data from proton-proton collisions at a centre-of-mass energy of $13$ TeV, recorded during Run 2 at the Large Hadron Collider and corresponding to integrated luminosities of 138-140 fb$^{-1}$. Searches are carried out for charged lepton flavour violation, baryon number violation and the presence of neutral heavy leptons. A precise measurement of lepton flavour universality between electrons and muons originating from top quark-antiquark events is also presented.