Group-Theoretical Property of Slightly Degenerate Fusion Categories of Certain Frobenius-Perron Dimensions

Abstract

Let p,q be odd primes, and let d be an odd square-free integer such that (pq,d) = 1. We show that slightly degenerate fusion categories of Frobenius-Perron dimensions 2p 2 q 2 d, 2p 2 q 3 d and 2p 3 q 3 d are group-theoretical.