Inner Semidirect Product Example: Dihedral Group

Semidirect products are very useful in group theory. To understand why, it's helpful to see an example. Here we show how to write the dihedral group D_2n as a semidirect product, and how we can describe that purely using cyclic groups!

0:00 Inner semidirect product
6:42 Abstract form
10:37 Example multiplication

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Music: C418 - Pr Department

[maximpushkar]

This videos helps me understand my algebra class! Thank you!

[nskeip]

Hi! Thanks for the video! There is one small detail I noticed. Seems like you proved that D lies in <r><s>, and there should be a prove that <r><s> lies in D as well.

UPD: oh but... if r and s belong to D, this is obvious)))

[dipenganguly]

Very nice explanation... Looking forward more videos from you...

[tomkerruish]

I'm surprised you didn't just use the general result that any subgroup of index 2 is automatically a normal subgroup. (Sketch of proof: if [G:H] = 2, then the only possible cosets of H are H and G - H, thus every left coset is a right coset, and so H is normal in G.) Of course, you know your audience better than I.
Are you in Ma5, or were you able to skip even further to Ma120? (A.k.a Ma5!)