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7. a) Let N G, H ≤ G. Let NH = = {nh: n € N, h E H}. Show that NH ≤ G. b) Let H ≤ G and [G:H]=2. Show that for every g E G, g² € H.

7. a) Let N G, H ≤ G. Let NH = = {nh: n € N, h E H}. Show that NH ≤ G. b) Let H ≤ G and [G:H]=2. Show that for every g E G, g² € H.

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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7. a) Let N G, H ≤ G. Let NH = {nh: n E N, h E H}. Show that NH ≤ G. b) Let H ≤ G and [G:H]=2. Show that for every g E G, g² € H.
Transcribed Image Text:7. a) Let N G, H ≤ G. Let NH = {nh: n E N, h E H}. Show that NH ≤ G. b) Let H ≤ G and [G:H]=2. Show that for every g E G, g² € H.
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