Geodesic
Burnside-type problems in discrete geometry
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 68-76.

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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.
Keywords: system of incidence, finite geometry, Burnside problem, weakened Burnside problem. 
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L. V. Kuz'min. Burnside-type problems in discrete geometry. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 68-76. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a5/

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