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

Abstract

We prove that modular categories of Frobenius–Perron dimension [Formula: see text] are solvable, where [Formula: see text] are prime numbers. As applications, we get that integral modular categories of Frobenius–Perron dimension less than [Formula: see text] are solvable, and hence integral perfect modular categories have Frobenius–Perron dimension greater than or equal to [Formula: see text]. 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 [Formula: see text].