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suppose G; A group and Hi 4 G;, For i.l,1 Give examples that violate the correctness of each of the following state ments. a)iř G,=G, and H,= Hz, Then H2 /G2 = Hyl Gq. b)iF G= G and He/ G2 es Hy/Gq.Then H2= Hq c) if H, /G, z H / G, and H, Hq.Then G,× Gq

suppose G; A group and Hi 4 G;, For i.l,1 Give examples that violate the correctness of each of the following state ments. a)iř G,=G, and H,= Hz, Then H2 /G2 = Hyl Gq. b)iF G= G and He/ G2 es Hy/Gq.Then H2= Hq c) if H, /G, z H / G, and H, Hq.Then G,× Gq

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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suppose G; A group and Hi 4 G;, For i-l," Give examples that violate the correctness of cach of the following statements. a) it Gz ,=G, and Hyz Hq , Then H2 IG, = Hq /Gq. 1 b)iF G,= G and He/ G2 as Hq / Gq.Then H2 x Hq 2 c) iF H2/G, = Hq / Gq and He x Hy.Then G Gy
Transcribed Image Text:suppose G; A group and Hi 4 G;, For i-l," Give examples that violate the correctness of cach of the following statements. a) it Gz ,=G, and Hyz Hq , Then H2 IG, = Hq /Gq. 1 b)iF G,= G and He/ G2 as Hq / Gq.Then H2 x Hq 2 c) iF H2/G, = Hq / Gq and He x Hy.Then G Gy
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