Let G be a finite abelian group. Then there exists a finite sequence of positive integers
Let G be a finite abelian group. Then there exists a finite sequence of positive integers
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Let G be a finite abelian group. Then there exists
a finite sequence of positive integers (p¹, p2²,... pr
which is unique but for the order of its elements, such
that P₁, P2,..., pr are primes (not necessarily distinct) and
α₁, α₂,..., α are positive integers (not necessarily distinct),
and
G = Z₁ Z₁
"P₁
α2
P2
+Z
ar
Pr](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa442f6dd-7f73-4607-864c-7b071db30feb%2F747ca4c1-323f-4678-b325-475ec0a8bbab%2Fod4dv6_processed.png&w=3840&q=75)
Transcribed Image Text:Let G be a finite abelian group. Then there exists
a finite sequence of positive integers (p¹, p2²,... pr
which is unique but for the order of its elements, such
that P₁, P2,..., pr are primes (not necessarily distinct) and
α₁, α₂,..., α are positive integers (not necessarily distinct),
and
G = Z₁ Z₁
"P₁
α2
P2
+Z
ar
Pr
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