<P><B>Abstract</B></P><P>Let <I>K</I> be an algebraic function field of one variable with constant field k and let C be the Dedekind domain consisting of all those elements of <I>K</I> which are in...
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https://www.riss.kr/link?id=A107532875
2006
-
SCI,SCIE,SCOPUS
학술저널
189-209(21쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
<P><B>Abstract</B></P><P>Let <I>K</I> be an algebraic function field of one variable with constant field k and let C be the Dedekind domain consisting of all those elements of <I>K</I> which are in...
<P><B>Abstract</B></P><P>Let <I>K</I> be an algebraic function field of one variable with constant field k and let C be the Dedekind domain consisting of all those elements of <I>K</I> which are integral outside a fixed place ∞ of <I>K</I>. We introduce “non-standard” automorphisms of the group <SUB><I>SL</I>2</SUB>(C), generalizing a result of Reiner for the special case <SUB><I>SL</I>2</SUB>(k[t]). For the (arithmetic) case where k is finite, we use these to transform congruence subgroups into non-congruence subgroups of almost any level. This enables us to investigate the existence, number, and minimal index of non-congruence subgroups of prescribed level. We provide also a group-theoretic characterization of those <SUB><I>SL</I>2</SUB>(C) where C is a principal ideal domain.</P>