Thread: D2n Isomorphic To Dn X Z2

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I'm using to represent the elements in and for those elements in . My first idea was to do this:

Map to since that forms a cyclic subgroup of the correct order.

Now I can't figure out where to go from here, or if my initial idea is even remotely in the ballpark.

Originally Posted by mathematicalbagpiper

Show that

I'm using to represent the elements in and for those elements in . My first idea was to do this:

Map to since that forms a cyclic subgroup of the correct order.

Now I can't figure out where to go from here, or if my initial idea is even remotely in the ballpark.

This result is only true when n is odd. In that case, it is correct to map to . The correspondence is completed by mapping to , and to (where is the identity element of ).