Burnside-type problems in discrete geometry
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Leonid V. Kuz’min
Abstract
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.
Originally published in Diskretnaya Matematika (2018) 30, №3, 68–76 (in Russian).
Acknowledgement
The author is grateful to the referee F. M. Malyshev for his comments, which contributed to significant improvements of the presentation.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Periodic properties of pushdown automata
- Burnside-type problems in discrete geometry
- On affine classification of permutations on the space GF(2)3
- Limit distributions of the maximal distance to the nearest neighbour
- Elementary transformations of systems of equations over quasigroups and generalized identities
- Asymptotics for the logarithm of the number of k-solution-free sets in Abelian groups
- On the distribution of multiple power series regularly varying at the boundary point
- A letter to the Editor
Artikel in diesem Heft
- Frontmatter
- Periodic properties of pushdown automata
- Burnside-type problems in discrete geometry
- On affine classification of permutations on the space GF(2)3
- Limit distributions of the maximal distance to the nearest neighbour
- Elementary transformations of systems of equations over quasigroups and generalized identities
- Asymptotics for the logarithm of the number of k-solution-free sets in Abelian groups
- On the distribution of multiple power series regularly varying at the boundary point
- A letter to the Editor
