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Question: problem 6 let g be a finite group a for...

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Problem 6. Let G be a finite group (a) For all a, b E G, show that ab and ba have the same order as elements of G. (b) For g є G define a function ф9 : G-> G by фд(h-ghg i for all h G. Show that Фд is a bijection, and that Og(ab)-Og(ao,(b). (c) If H is a subgroup of G, show that фд(11)-tog(h) : h є Н} is also a subgroup of G.

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