caa a22 4500 388108533 CHVBK 20180307125346.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500027475 doi S0308210500027475 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500027475 Mason A. W. Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK (awm@maths.gla.ac.uk) Free quotients of infinite rank of GL2 over Dedekind domains [Elektronische Daten] [A. W. Mason] This paper is concerned with integral domains R, for which the factor group SL2(R)/U2(R) has a non-trivial, free quotient, where U2(R) is the subgroup of GL2(R) generated by the unipotent matrices. Recently, Krstić and McCool have proved that SL2(P[x])/U2(P[x]) has a free quotient of infinite rank, where P is a domain which is not a field. This extends earlier results of Grunewald, Mennicke and Vaserstein. Any ring of the type P[x] has Krull dimension at least 2. The purpose of this paper is to show that result of Krstić and McCool extends to some domains of Krull dimension 1, in particular to certain Dedekind domains. This result, which represents a two-dimensional anomaly is the best possible in the following sense. It is well known that SL2(R) = U2(R), when R is a domain of Krull dimension zero, i.e. when R is a field. It is already known that for some arithmetic Dedekind domains A, the factor group SL2(A)/U2(A) has a free quotient of finite (and not infinite) rank. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 77-84 0308-2105 129:1<77 1999 129 PRM https://doi.org/10.1017/S0308210500027475 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500027475 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mason A. W. Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK (awm@maths.gla.ac.uk) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 77-84 0308-2105 129:1<77 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge