A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\). (English. Russian original) Zbl 1409.51006
Sib. Math. J. 59, No. 2, 309-322 (2018); translation from Sib. Mat. Zh. 59, No. 2, 396-411 (2018).
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.
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.
Reviewer: Hubert Kiechle (Hamburg)
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