Some properties of group-theoretical categories

摘要

We first show that every group-theoretical category is graded by acertain double coset ring. As a consequence, we obtain a necessaryand sufficient condition for a group-theoretical category to benilpotent. We then give an explicit description of the simple objectsin a group-theoretical category (following 1021) and of the groupof invertible objects of a group-theoretical category, in group-theoretical terms. Finally, under certain restrictive conditions,we describe the universal grading group of a group-theoreticalcategory.