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In characteristic zero, quotient singularities are log terminal. Moreover, wecan check whether a quotient variety is canonical or not by using only the ageof each element of the relevant finite group if the group does not havepseudo-reflections. In positive characteristic, a quotient variety is not logterminal, in general. In this paper, we give an example of the quotient varietywhich is not log terminal such that the quotient varieties associated to anyproper subgroups are canonical. In particular, we cannot determine whether agiven quotient singularity is canonical by looking at proper subgroups.

Pathological quotient singularities in characteristic three which are not log canonical