On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.

1989 ◽  
Vol 1989 (402) ◽  
pp. 138-152
Keyword(s):  
Congruence Subgroup ◽  
Algebraic Groups ◽  
Number Fields ◽  
Subgroup Problem ◽  
Congruence Subgroup Problem

scholarly journals Solution of the congruence subgroup problem for solvable algebraic groups

1980 ◽  
Vol 79 ◽  
pp. 141-144 ◽  
Author(s):  
Jasbir Singh Chahal
Keyword(s):  
Congruence Subgroup ◽  
Algebraic Groups ◽  
Algebraic Number Field ◽  
Rational Numbers ◽  
Finite Degree ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Universal Domain ◽  
Subgroup Problem ◽  
Congruence Subgroup Problem

Let k be an algebraic number field of finite degree over the field Q of rational numbers. We denote by o the ring of integers in k. In general, for a subring A, containing 1, of a universal domain Ω we denote by GL(n, A) the subgroup of GL(n, Ω) consisting of matrices x = (xij) with xij ∈ A and det x ∈ A×, the group of units of A. Now, we consider an algebraic group G in GL(n, Ω) defined over k.

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