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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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/

[1] Z. I. Borevich, “O podgruppakh lineinykh grupp, bogatykh transvektsiyami”, Zap. nauch. seminarov LOMI, 75, 1978, 22–31 | MR | Zbl

[2] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1982 | MR | Zbl

[3] V. M. Levchuk, “Zamechanie k teoreme L. Diksona”, Algebra i logika, 22:5 (1983), 504–517 | MR | Zbl

[4] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, Izdanie 17-e, Novosibirsk, 2010

[5] V. A. Koibaev, “Seti, assotsiirovannye s elementarnymi setyami”, Vladikavkazskii mat. zhurn., 12:4 (2010), 39–43 | MR | Zbl

[6] V. A. Koibaev, “Elementarnye seti v lineinykh gruppakh”, Trudy Instituta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 134–141

[7] Ya. N. Nuzhin, “Faktorizatsiya kovrovykh podgrupp grupp Shevalle nad kommutativnymi koltsami”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 527–535