  The origin of large-scale magnetic fields, detected in some low-mass (dwarf
and irregular) galaxies via polarised synchrotron emission and Faraday
rotation, remained unexplained for a long time. We suggest that mean-field
dynamo can be active in galaxies of this class despite their slow rotation
because their discs are relatively thick. Earlier assessments of the
possibility of the mean-field dynamo action in low-mass galaxies relied on
estimates applicable to $\textit{thin}$ discs, such as those in massive spiral
galaxies. Using both order-of-magnitude estimates and numerical solutions, we
show that the strength of differential rotation required to amplify magnetic
field reduces as the aspect ratio of the galactic gas layer increases. Thus,
the puzzle of the origin of large-scale magnetic fields appears to be solved.
As a result, this class of galaxies provides a new ground for testing our
understanding of galactic magnetism.
