Geodesic
Decomposition of transvection in elementary group
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 388-392

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The elementary net (elementary carpet) $\sigma=(\sigma_{ij})$ an order 3 of additive subgroups commutative ring is considered, the derivative net $\omega$ connected with it, elementary group $E(\sigma)$ and net group $G(\omega)$. It is proved that a elementary transvection $t_{ij}(\alpha)$ from $E(\sigma)$ is a product of a matrix from group $\langle t_{ij}(\sigma_{ij}),t_{ji}(\sigma_{ji})\rangle$ and matrixes from $G(\omega)$.
Mots-clés : net, net group, transvection.
Keywords: carpet, elementary nets, carpet group, elementary group 
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     author = {Vladimir A. Koibaev},
     title = {Decomposition of transvection in elementary group},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a10/}
}
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Vladimir A. Koibaev. Decomposition of transvection in elementary group. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 388-392. http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a10/