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## Homework Statement

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?