Abstract
In 1976, in the special course on Projective Planes given at Novosibirsk State University, and later in 1977, in the report on Projective Planes given at the Fourteenth All-Union Algebra Conference, A.I. Shirshov presented the concept of a projective plane as a partial algebraic system. This approach allowed the formulation of a number of new problems, together with a new viewpoint on known results and problems in the theory of projective planes. In the present work, we discuss part of the results contained in the special course and in the report, and also some further developments.
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References
A. Giovagnoli, Sulla rappresentazione di un piano libero mediante una classe di simboli, Rend. Mat. e Appl. 25, 3–4 (1966) 427–438.
M. Hall, Projective planes, Trans. Amer. Math. Soc. 54 (1943) 229–277.
D.R. Hughes and F.C. Piper, Projective Planes, Graduate Texts in Mathematics 6, Springer-Verlag, New York-Berlin, 1973.
N.L. Johnson, Homomorphisms of free planes, Math. Z. 125 (1972) 255–263.
K.H. Kim and F.W. Roush, A universal algebra approach to free projective planes, Aequationes Math. 19, 1 (1979) 48–52.
L.I. Kopeikina, Free decompositions of projective planes, Izv. Akad. Nauk SSSR Ser. Mat. 9, 1 (1945) 495–526.
R. Magari, Su una classe di simboli atta a rappresentare gli elementi di un piano grafico e su un teorema di riduzione a forma normale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 33, 1 (1962) 37–44.
G. Pickert, Projektive Ebenen, Die Grundlehren der mathematischen Wissenschaften LXXX, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955.
G. Pickert, Projektive Ebenen, Zweite Auflage, Die Grundlehren der Mathematischen Wissenschaften 80, Springer-Verlag, Berlin-New York, 1975.
L.A. Skornyakov, Projective planes, Uspekhi Mat. Nauk 6, 6 (1951) 112–154.
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Shirshov, A.I., Nikitin, A.A. (2009). On the Theory of Projective Planes. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_19
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DOI: https://doi.org/10.1007/978-3-7643-8858-4_19
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