We give a necessary condition for Galois covering singularities to be logterminal or -canonical singularities, which is also sufficient under acertain restriction on the branch loci of the covering maps. We also give a method constructing explicitly resolutions of 2-dimensional Abel covering singularities.
Hiroyasu TSUCHIHASHI. "Galois covering singularities I." J. Math. Soc. Japan 51 (1) 35 - 44, January, 1999. https://doi.org/10.2969/jmsj/05110035