On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.
G. Tomanov (1989)
Journal für die reine und angewandte Mathematik
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On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.
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We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.