Talk:Dihedral Group D4/Subgroups

Potential Error?

Twitter claims that "Missing the subgroup ${e, a², ba, ba³}$ of the dihedral group $D₄$" — https://twitter.com/shropium/status/1322316703867416577 --Joe (talk) 15:07, 2 November 2020 (UTC)

Good call. Missed that one.

It occurs to me that we can (ought to?) develop the last two subgroups by taking the group product of $\set {e, a^2}$ with $\set {e, b}$ and $\set {e, b a}$ respectively.

In fact, we probably really ought to create the group product of all the order $2$ subgroups with all the other order $2$ subgroups and see where that takes us, and thence demonstrate that all group direct products of subgroups results in the same $2$ viergruppen.

Work in progress. --prime mover (talk) 16:25, 2 November 2020 (UTC)