Semifield planes of odd order that admit a subgroup of autotopisms isomorphic to \(A_4\). (English. Russian original) Zbl 1358.51005
Russ. Math. 60, No. 9, 7-22 (2016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 9, 10-25 (2016).
The author describes odd-order semifield planes admitting a Baer involution or an alternating group \(A_{4}\) in the translation complement.
Explicit matrix representations of the spreads are given. The results are applied to the order \(81\) case.
The reviewer is surprised not to find any references to papers after the year 2000, from outside the authors work group. Certainly relevant would be, e.g., [U. Dempwolff, J. Geom. 89, No. 1–2, 1–16 (2008; Zbl 1175.12003)].
Explicit matrix representations of the spreads are given. The results are applied to the order \(81\) case.
The reviewer is surprised not to find any references to papers after the year 2000, from outside the authors work group. Certainly relevant would be, e.g., [U. Dempwolff, J. Geom. 89, No. 1–2, 1–16 (2008; Zbl 1175.12003)].
Reviewer: Hubert Kiechle (Hamburg)
MSC:
| 51E15 | Finite affine and projective planes (geometric aspects) |
| 51A40 | Translation planes and spreads in linear incidence geometry |
| 51E23 | Spreads and packing problems in finite geometry |
Keywords:
semifield plane; spread set; Baer involution; isomorphism; autotopism; collineation group; alternating groupCitations:
Zbl 1175.12003References:
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