Geodesic
Elementary nets in linear groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 134-141
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For an elementary net (a net without diagonal) of additive subgroups of an arbitrary commutative ring, we define a derivative net, the closure of the net, and a net associated with the elementary group. A factorization of the elementary group is presented and used to construct an example of a closed (admissible) net that cannot completed to the (complete) net.
Mots-clés : net, net group, transvection.
Keywords: elementary net, closed net, elementary group 
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V. A. Koibaev. Elementary nets in linear groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 134-141. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a14/

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

[2] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1982, 288 pp. | MR | Zbl

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

[4] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, Izd. 17-e, dop., In-t matematiki SO RAN, Novosibirsk, 2010, 219 pp. URL: http://math.nsc.ru/~alglog/17kt.pdf

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