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On the group $SL_2$ over Dedekind rings of arithmetic type

L. N. Vaserstein


Abstract: 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.

UDC: 519.443

MSC: Primary 20H05, 15A33; Secondary 10M20

Received: 13.12.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 18:2, 321–332

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