Did you mean: Decomposition Finite Abelian Groups
Any finite Abelian group can be decomposed as a direct sum of cyclic subgroups of prime power order.
Jan 5, 2001 · This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden ...
A nontrivial finite abelian group is a direct sum of indecomposable subgroups. Proof. This argument will be the same as the standard proof of the existence of ...
People also ask
What is the primary decomposition of finite abelian groups?
What is a finite abelian group isomorphic to?
Are all finite abelian groups solvable?
How to find finite abelian groups?
Every finite abelian group is finitely generated. The finitely generated abelian groups can be completely classified.
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups. Such a decomposition is needed ...
Jul 28, 2013 · The two standard decompositions for a finitely generated abelian group (or more generally modules over a PID) are invariant factor decomposition and elementary ...
A quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups and leading to an efficient algorithm for computing ...
In this module we prove that every finite abelian group can be expressed as an internal direct product of a family of p-primary subgroups.
The Primary Decomposition Theorem uses the Fundamental Theorem of Arithmetic to represent the order of a group as a product of primes. The group can then be ...
Oct 25, 2020 · The Fundamental Theorem of Finite Abelian Groups states that every finite abelian group can be decomposed into a direct product of cyclic groups ...