Three-dimensional isolated quotient singularities in odd characteristic

Let a finite group $G$ act linearly on a finite-dimensional vector space $V$ over an algebraically closed field $k$ of characteristic $p>2$. Suppose that the quotient space $V/G$ has an isolated singularity only. The isolated singularities of the form $V/G$ are completely classified in the case when $p$ does not divide the order of $G$, and their classification reduces to Vincent's classification of isolated quotient singularities over $\mathbb C$. In the present paper we show that, if $\dim V=3$, then the classification of isolated quotient singularities reduces to Vincent's classification in the modular case as well (when $p$ divides $|G|$). Some remarks on quotient singularities in other dimensions and in even characteristic are also given.
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