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Exercise 7.16. Prove that if N is a normal subgroup of the finite group G and ged(|N|, |G/N|) = 1, then N is the unique subgroup of G with order |N|.

Exercise 7.16. Prove that if N is a normal subgroup of the finite group G and ged(|N|, |G/N|) = 1, then N is the unique subgroup of G with order |N|.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please avoid Sylow's theorem or more advanced theorems as I am not familiar and explain steps. Thanks!

Exercise 7.16. Prove that if N is a normal subgroup of the finite group G and ged(|N|, |G/N]) = 1, then N is the unique subgroup of G with order |N|.
Transcribed Image Text:Exercise 7.16. Prove that if N is a normal subgroup of the finite group G and ged(|N|, |G/N]) = 1, then N is the unique subgroup of G with order |N|.
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