Let G be any group and n>1 a fixed integer such that (xy)n=xnyn for all x,y...

Question

Question

Let G be any group and n>1 a fixed integer such that (xy)ⁿ=xⁿyⁿ for all x,y in G .

H={ aⁿ , a belong to G }

show that H is a normal subgroup .

math algebra

Answer 1

Answer #1

Ans: The map f: GYG with f(2)=& ho all REG. The condition (hy) = 2 yn tell us that f is homo-ooptism. Gh is the image of f

Answer 2

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