journey85
Sep10-08, 02:30 PM
1. The problem statement, all variables and given/known data
The dihedral group D2n has elements e, x, x2, ..., xn-1, y, xy, x2y, ..., xn-1y and relations xn=e, y2=e (where e is identity) and yx=xn-1y
(a) Show that D2n={ elements listed above} i.e. show that these elements are distinct
(b) Show that xy=yxn-1
(c) Is there an integer m between 1, ..., n-1 such that yxm=xmy?
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?
The dihedral group D2n has elements e, x, x2, ..., xn-1, y, xy, x2y, ..., xn-1y and relations xn=e, y2=e (where e is identity) and yx=xn-1y
(a) Show that D2n={ elements listed above} i.e. show that these elements are distinct
(b) Show that xy=yxn-1
(c) Is there an integer m between 1, ..., n-1 such that yxm=xmy?
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?