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On Subplanes of Free Planes

Published online by Cambridge University Press:  20 November 2018

Reuben Sandler
Reuben Sandler*
Affiliation:
Institute for Defense Analyses Princeton, New Jersey
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In 1945, L. I. Kopejkina (4), at the suggestion of A. G. Kurosh, began a programme of studying the properties of free projective planes and the analogies between free planes and free groups. In this paper, this study will be extended by proving a tool theorem and several of its consequences. The theorem deals with the existence of "minimal free generators" for subplanes of free planes.

A set of points and lines and an incidence relation are said to form a projective plane if the following three axioms are satisfied.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 379 - 385
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Dembowski, Peter, Freie unà offerte projektive Ebenen, Math. Z., 72 (1960), 410–438.Google Scholar
2. F, H.édérer and Jonsson, B., Some properties of free groups, Trans. Amer. Math. Soc, 68 (1950), 1–27.Google Scholar
3. Hall, M., Projective planes, Trans. Amer. Math. Soc, 54 (1943), 229–277.Google Scholar
4. Kopejkina, L. I., Decomposition of projective planes, Izv. Akad. Nauk, SSSR, Sec. Math., 9 (1945), 495–526.Google Scholar
5. Reuben Sandler, The collineation groups of free planes, Trans. Amer. Math. Soc, 107 (1963), 129–139.Google Scholar
6. Skornyakov, L. A., Projective planes, Translations Amer. Math. Soc, Ser. 1, 1 (1962), 51–107.Google Scholar
7. Specht, Wilhelm, Gruppentheorie (Berlin, 1956).Google Scholar