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# Show that there exist an injective homomorphism of dihedral group $D_n$ into $G$.

Let $$n>2$$ and the group $$(G,⋅)$$. Consider that there existe $$a,b∈G$$ such that $$a^n=b^2=1_G$$ and $$b⋅a=a^{−1}⋅b$$ and $$n$$ is the smallest $$n≥1$$ such that $$a^n=1_G$$. Show that there exist an injective homomorphism of dihedral group $$D_n$$ into $$G$$.

I know that the dihedral group $$D_n$$ has the same properties ($$a,b∈G$$ such that $$a^n=b^2=1_G$$ and $$b⋅a=a^{−1}⋅b$$) as the group $$(G,⋅)$$.

I can't find a such injective homomorphism of dihedral group $$D_n$$ into $$G$$. Does someone could help me?

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