This research explores conjugacy classes in finite groups and their influence on modular fusion categories, highlighting new dimensions.
The influence of certain arithmetic conditions on the sizes of conjugacy classes of a finite group on the group structure has been extensively studied in recent years. In this paper, we explore analogous properties for fusion categories. In particular, we establish an Ito-Michler-type result for modular fusion categories.
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Sebastian Burciu (2025) studied this question.
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