The radio pulsar and rotating radio transient populations are only known in and near the Milky Way. Investigating such populations in other galaxies requires deep pulsar and transient searches. We performed 4-h radio observations of nearby galaxies M33, M81 and M82 with LOFAR. Our main purpose was to characterise the bright end of the pulsar population in other galaxies, and compare it to that of the Milky Way. We searched for extragalactic radio pulsars through a periodic-pulse search, and for sporadic fast radio transients through a single-pulse search. We coherently combined at most 23 LOFAR Core High-Band Antenna (HBA) stations and covered M33, M81, and M82 in their entirety using multiple tied-array beams. No pulsating sources or single pulses were found. We have, therefore established stricter limits on the extragalactic pulsar flux density at lower frequencies than those obtained in previous Arecibo, GBT, and WSRT searches. We conclude that in nearby galaxies M33, M81, and M82 there are no pulsars shining toward Earth with pseudo luminosities greater than a few times that of the brightest pulsars in our Milky Way.
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