Information om | Engelska ordet ABELIANIZATION

Exempel på hur man kan använda ABELIANIZATION i en mening

• Artin's reciprocity law implies a description of the abelianization of the absolute Galois group of a global field K that is based on the Hasse local–global principle.
• In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial).
• A consequence is that the kernel of the Artin map is the connected component of the identity of the idele class group, so that the abelianization of the Galois group of F is the profinite completion of the idele class group.
• In more classical terms, a superperfect group is one whose abelianization and Schur multiplier both vanish; abelianization equals the first homology, while the Schur multiplier equals the second homology.

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