A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\)
Consider a semifield plane \(\pi\) of order \(p^{N}\), \(p>2\) a prime. The authors prove: If the autotopism group of \(\pi\) contains \(A_{5}\), and is in particular non solvable, then \(N=4n\) and the matrices describing spread sets that defines \(\pi\) have a special form described in the paper. If \(p\equiv 1\pmod 4\), then this cannot happen. The authors use elaborate calculations with matrices inside the spread sets.
scientific article; zbMATH DE number 6908380