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Without using the structure theorem for finite abelian groups, prove that a finite abelian group has an element of order p for every prime p that divides |G|. It is OK to follow the proof in the text, but write in your own words, and make sure you understand what your are writing.

Without using the structure theorem for finite abelian groups, prove that a finite abelian group has an element of order p for every prime p that divides |G|. It is OK to follow the proof in the text, but write in your own words, and make sure you understand what your are writing.

Advanced Engineering Mathematics
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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Without using the structure theorem for finite abelian groups, prove that a finite abelian group has an element of order p for every prime p that divides |G|. It is OK to follow the proof in the text, but write in your own words, and make sure you understand what your are writing.
Transcribed Image Text:Without using the structure theorem for finite abelian groups, prove that a finite abelian group has an element of order p for every prime p that divides |G|. It is OK to follow the proof in the text, but write in your own words, and make sure you understand what your are writing.
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