finite abelian group造句

• Clearly, every finite abelian group is finitely generated.
• This gave a finite abelian group, as was recognised at the time.
• In general, a finite abelian group " G " is considered.
• The automorphism group of a finite abelian group can be described directly in terms of these invariants.
• The families of finite Abelian groups and finite nilpotent groups are almost full, but neither full nor Melnikov.
• It follows that any finite abelian group " G " is isomorphic to a direct sum of the form
• If G is a finite abelian group, then G \ cong \ widehat { G } but this isomorphism is not canonical.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, from which many other basic concepts, such as non-abelian counterparts, and finite abelian groups are very well understood.
• This further generalizes to the fact that in any finite abelian group, either the product of all elements is the identity, or there is precisely one element " a " of order 2 ( but not both ).
• We may define the Fourier transform for finite abelian groups for an element f \ in \ widehat { G } as the function \ widehat { f } : \ widehat { G } \ to \ mathbb { C } given by
• As a consequence, one can prove that in a finite abelian group, if " m " denotes the maximum of all the orders of the group's elements, then every element's order divides " m ".