Projective Planes with a Regular Collineation Group and a Question about Powers of a Prime

The nonexistence of projective planes of

The nonexistence of projective planes of order 12 with a collineation group of order 8

✍ Kenzi Akiyama; Chihiro Suetake 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB

## Abstract In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}\_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. A