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On Desargues geometrization of the characteristic of a skew field. (Russian) Zbl 1026.51001

Summary: The paper contains: (1) Desargues geometrization of characteristic \(p\geq 5\) of a field given as a configuration theorem \(K_p\) and involving a pair of perspective \(p\)-gones with center \(S\) and axis \(l\) such that \(S\in l\); (2) Desargues geometrization of characteristics 2 or 3 of skew fields given as configuration theorems \(D^*_8(\bar{1}\bar{2}\bar{3},\overline{1'} \overline{2'} \overline{3'})\) or \(L_7(\bar{1}\bar{2}\bar{3},\overline{1'} \overline{2'} \overline{3'})\) respectively; (3) proofs of the following theorems: “\(L_{10}\Rightarrow K_p\)”, “\(7_3\Rightarrow D^*_8\)”, “\(L_7\Leftrightarrow 8_3\)”, and “\(K_p\Leftrightarrow p=0\)”.

MSC:

51A20 Configuration theorems in linear incidence geometry
51A30 Desarguesian and Pappian geometries
51E20 Combinatorial structures in finite projective spaces
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