EXPLORATION OF FINITE GROUP APPROACH IN BALANCED INCOMPLETE BLOCK DESIGN

The development of block designs continues to be an unresolved challenge in combinatorial design, with several forms, the most notable being the balanced incomplete block designs (BIBDs). This study evaluates the existence of BIBDs using an algebraic approach to verify whether these designs satisfy the postulates of finite groups. Both symmetric and non-symmetric BIBDs are analyzed, and theorems were established in line with finite group theory. Findings reveal that BIBDs are not finite groups under multiplicative binary operations, and it form abelian additive groups under addition, thereby confirming their algebraic consistence with the concept of finite groups.