Frobenius-Perron Dimensions of Conjugacy Classes and an Ito-Michler-Type Result in Modular Fusion Categories

Key Points

• The study establishes an Ito-Michler-type result for modular fusion categories, expanding existing theories.
• Key finding reveals that arithmetic conditions critically affect the sizes of conjugacy classes in group structures.
• This exploration of fusion categories provides insights into the mathematical behavior of conjugacy classes over finite groups.
• The findings aim to bridge relationships between group theory and fusion categories, promoting deeper understanding in both areas.