Modular categories of Frobenius–Perron dimension p2q2r2 and perfect modular categories.

We prove that modular categories of Frobenius–Perron dimension p 2 q 2 r 2 are solvable, where p < q < r are prime numbers. As applications, we get that integral modular categories of Frobenius–Perron dimension less than 1 8 0 0 are solvable, and hence integral perfect modular categories have Frobenius–Perron dimension greater than or equal to 1 8 0 0. When the modular categories considered are weakly group-theoretical, we further prove that integral perfect modular categories have Frobenius–Perron dimension greater than or equal to 3 6 0 0. [ABSTRACT FROM AUTHOR]