Premium
The Minimum Index of a Non‐Congruence Subgroup of SL 2 Over an Arithmetic Domain. II: The Rank Zero Cases
Author(s) -
Mason A. W.,
Schweizer Andreas
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704006027
Subject(s) - mathematics , sl2(r) , congruence subgroup , congruence (geometry) , combinatorics , normal subgroup , arithmetic , rank (graph theory) , zero (linguistics) , group (periodic table) , geometry , linguistics , chemistry , philosophy , organic chemistry
Let K be a function field of genus g with a finite constant field F q . Choose a place ∞ of K of degree δ and let C be the arithmetic Dedekind domain consisting of all elements of K that are integral outside ∞. An explicit formula is given (in terms of q, g and δ) for the minimum index of a non‐congruence subgroup in SL 2 ( C ). It turns out that this index is always equal to the minimum index of an arbitrary proper subgroup in SL 2 ( C ). The minimum index of a normal non‐congruence subgroup is also determined.