Flag-transitive and point-primitive block designs and orthogonal groups of odd dimension

Key Points

• To classify nontrivial 2-designs with specific automorphism groups of odd dimension.
• Analyzed properties of flag-transitive and point-primitive block designs.
• Investigated groups of almost simple type and their socles.
• Focused on orthogonal simple groups in odd dimensions.
• Identified key characteristics of block designs and their automorphism groups.
• Provided insights into the structure of orthogonal groups on odd dimensions.