Geodesic
On closure of configurations in freely generated projective planes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 358-368

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Let $\mathcal{F}$ be an arbitrary freely generated projective plane. Based on Shirshov's combinatorial method, we introduce the notion of a reduced configuration in $\mathcal{F}$. We prove that for every subplane $\mathcal{P}$ generated in $\mathcal{F}$ by some configuration $\mathcal{B}$, there is a reduced configuration $\mathcal{B}'$ such that $\mathcal{P}$ is freely generated by $\mathcal{B}'$.
Keywords: projective plane, incidence, freely generated projective plane, nonassociative word, regular word.
Mots-clés : configuration 
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     author = {N. T. Kogabaev},
     title = {On closure of configurations in freely generated projective planes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {358--368},
     publisher = {mathdoc},
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     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a5/}
}
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N. T. Kogabaev. On closure of configurations in freely generated projective planes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 358-368. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a5/