Group-theoretical property of non-degenerate fusion categories of FP-dimension $p^2q^3$ and $p^3q^3$

Abstract

In this paper, we show that non-degenerate fusion categories of FP-dimensions $p^2q^3d$ and $p^3q^3d$ are group-theoretical, where $p, q$ are odd primes, $d$ is a square-free integer such that $(pq,d) = 1$.