# finite abelian group in a sentence

1. Clearly, every finite abelian group is finitely generated.
2. This gave a finite abelian group, as was recognised at the time.
3. In general, a finite abelian group " G " is considered.
4. The automorphism group of a finite abelian group can be described directly in terms of these invariants.
5. The families of finite Abelian groups and finite nilpotent groups are almost full, but neither full nor Melnikov.
6. It's difficult to find finite abelian group in a sentence.
7. It follows that any finite abelian group " G " is isomorphic to a direct sum of the form
8. If G is a finite abelian group, then G \ cong \ widehat { G } but this isomorphism is not canonical.
9. The fundamental theorem of finite abelian groups states that every finite abelian group can be expressed as the direct sum of cyclic subgroups of prime-power order.
10. The fundamental theorem of finite abelian groups states that every finite abelian group can be expressed as the direct sum of cyclic subgroups of prime-power order.
11. When " G " is a finite abelian group, the group ring is commutative, and its structure is easy to express in terms of roots of unity.
12. The fundamental theorem of finitely generated abelian groups states that a finitely generated abelian group is the rank and a finite abelian group, each of which are unique up to isomorphism.
13. reduced the principal ideal theorem to a question about finite abelian groups : he showed that it would follow if the transfer from a finite group to its derived subgroup is trivial.
14. An arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants.
15. Clearly Carmichael's theorem is related to Euler's theorem, because the exponent of a finite abelian group must divide the order of the group, by elementary group theory.
16. Direct sums play an important role in the classification of abelian groups : according to the fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the direct sum of cyclic groups.
17. More:   1  2

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