Please help with number 37 using only the definitions of isomorphism if possible. 36. Exhibit two groups of the same finite order that are not isomorphic.37. Let o be an isomorphism from group G to group H. Let x be in G. Prove that 4(x") =($(x))" for every integer n.38. If G and H are groups and (: G → H is an isomorphism, prove that a and ø(a) havethe same order, for any a E G.

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Answered: 37.) Let o be an isomorphism from group…

37.) Let o be an isomorphism from group G to group H. Let x be in G. Prove that $(x") : (6(x))" for every integer n. 38 IE G and H are grouns and d: G H ie o that a and bla) have

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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Question

Please help with number 37 using only the definitions of isomorphism if possible.

36. Exhibit two groups of the same finite order that are not isomorphic.
37. Let o be an isomorphism from group G to group H. Let x be in G. Prove that 4(x") =
($(x))" for every integer n.
38. If G and H are groups and (: G → H is an isomorphism, prove that a and ø(a) have
the same order, for any a E G.

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