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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

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