Geodesic
On the group $SL_2$ over Dedekind rings of arithmetic type
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 321-332 
L. N. Vaserstein. On the group $SL_2$ over Dedekind rings of arithmetic type. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 321-332. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the group of matrices of order two with determinant 1 over a Dedekind ring of arithmetic type is generated by elementary matrices if there are infinitely many invertible elements in this ring. We also obtain a more general result, describing the group generated by elementary matrices belonging to a congruence subgroup. Bibliography: 6 titles.

[1] X. Base, Dzh. Milnor, Zh.-P. Serr, “Reshenie kongruentsproblemy dlya $SL_n$ ($n\geqslant3$) i $Sp_{2^n}$ ($n\geqslant2$)”, Matematika, 14:6 (1970); 15:1 (1971), 44–60

[2] Zh.-P. Serr, “Problema kongruentspodgrupp dlya $SL_2$”, Matematika, 15:6 (1971), 12–45 | Zbl

[3] O'Meara, “On the finite generation of linear groups over Hasse domains”, J. Reine und Angew. Math., 217 (1965), 79–108 | MR | Zbl

[4] C. Moore, “Group extensions of $p$-adic and adelic linear groups”, Publ. Math., 35 (1968), 5–70 | MR | Zbl

[5] P. M. Cohn, “On the structur of the $GL_2$ of a ring”, Publ. Math., 30 (1966), 365–413 | MR | Zbl

[6] L. N. Vasershtein, “$K_1$-teoriya i kongruentsproblema”, Matem. zametki, 5:2 (1969), 233–244