On coset cenral Schur rings

Key Points

• To establish the conditions under which a central Schur ring is also a coset Schur ring within finite groups.
• Proved several equivalent conditions for central Schur rings to be coset Schur rings.
• Utilized algebraic constructions related to group actions.
• Provided clear conditions linking central and coset Schur rings.
• Demonstrated that the conjugation action plays a significant role in this relationship.