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Burnside-type problems in discrete geometry. (English. Russian original) Zbl 1496.51002

Discrete Math. Appl. 29, No. 6, 357-362 (2019); translation from Diskretn. Mat. 30, No. 3, 68-76 (2018).
Summary: The paper is concerned with systems of incidence involving a space of points \(X\) and lines consisting of \(q\) points each. A free space \(X\) is defined. For a space \(X\) an analogue of the Burnside problem (solved in the negative) and an analogue of the weakened Burnside problem are formulated. In the case \(q = 3\) the positive answer to the analogue of the weakened Burnside problem is equivalent to the existence of a universal finite geometry.

MSC:

51A05 General theory of linear incidence geometry and projective geometries
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References:

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