I'm no mathematician, but maybe plurals (?) "Dihedrals", " cyclics", etxc. sound fine to me, but I'm no expert.
this post was submitted on 23 Feb 2024
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it's more about linguistics and it is clearly what mathematicians in the past didn't care enough, so it is okay to talk about it and give ideas.
Cyclicorgy, dihedralorgy, etc...
Just omit the word group