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The dihedral group D_{2n}has elements e, x, x^{2}, ..., x^{n-1}, y, xy, x^{2}y, ..., x^{n-1}y and relations x^{n}=e, y^{2}=e (where e is identity) and yx=x^{n-1}y

(a) Show that D_{2n}={ elements listed above} i.e. show that these elements are distinct

(b) Show that xy=yx^{n-1}

(c) Is there an integer m between 1, ..., n-1 such that yx^{m}=x^{m}y?

The problem I have is simply getting started as it's been so long since I've had any type of linear algebra/modern algebra courses.. If anyone could help me get started on this problem I'd greatly appreciate it.. How does one prove distinction?

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# Homework Help: Distinct elements and relations

Can you offer guidance or do you also need help?

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