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Exercise 6(@) Prove thal the add.tive Z oud Q are not isomonpkic (6) Show that there are non groups somonphic groups ef ordor4

Exercise 6(@) Prove thal the add.tive Z oud Q are not isomonpkic (6) Show that there are non groups somonphic groups ef ordor4

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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Modern Algebra: Group Theory

 

the additive hic are net is ononphic (6) Show that there are non Exercise 6 (a) Prove that grouns Z oud Q Z and Q are non-isomonphic groups of order4 onder4
Transcribed Image Text:the additive hic are net is ononphic (6) Show that there are non Exercise 6 (a) Prove that grouns Z oud Q Z and Q are non-isomonphic groups of order4 onder4
Expert Solution
Step 1

If G and H are isomorphic then G is cyclic if and only if H is cyclic.

So if G is cyclic but H is non cyclic then G and H are non isomorphic.

Also if G and H are cyclic then G has an element of order n if and only if H has an element of order n.

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