Projektivitätengruppen von Ebenen über endlichen Semikörpern. (On groups of projectivities of planes over finite semi-fields) (Q803937)

The author proves for finite semifields S: 1) If S is non-associative and of odd order, then the projective plane over S has the symmetric group of \(card(S)+1\) letters as its group of projectivities. [See \textit{J. Joussen}, Abh. Math. Semin. Univ. Hamb. 35, 230-241 (1971; Zbl 0216.430) for the nearfield situation.] 2) In some cases (for instance: if the cardinality of the kernel K of S is prime or the square of a Mersenne prime number) the group of projectivities of the affine plane over S is shown to coincide with the affine group of the K-vectorspace S, thus giving rise to the conjecture that this will be true in general.