Question 9: a. Let G be an Abelian group, let a, bEG: |a| = |b| = 2. {e, b}. Show that HK ≤ G and Let H= {e, a} and K |G| = 4m, m E Z. = b. Conclude that HK is normal subgroup of G.
Question 9: a. Let G be an Abelian group, let a, bEG: |a| = |b| = 2. {e, b}. Show that HK ≤ G and Let H= {e, a} and K |G| = 4m, m E Z. = b. Conclude that HK is normal subgroup of G.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Question 9:
a. Let G be an Abelian group, let a, b E G: |a| = |b| = 2.
Let H = {e, a} and K = {e, b}. Show that HK ≤ G and
|G| = 4m, me Z.
b. Conclude that HK is normal subgroup of G.
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