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Nov 30, 2020 at 13:30 comment added YCor By the way a single conjugacy class is syndetic in this example: $AB^G=G$ where $B=\{s\}$ and $A=\{1,st,s,t\}$.
Nov 30, 2020 at 13:27 comment added Ville Salo The fact this is virtually cyclic is extra interesting for my application, so double thanks.
Nov 30, 2020 at 13:09 vote accept Ville Salo
Nov 30, 2020 at 13:08 comment added Ville Salo Or maybe the dihedral group is a monster group, this is not the first time it is a counterexample to a property I figured all natural groups should have (e.g. splendidness from my other MO post).
Nov 30, 2020 at 13:07 comment added Ville Salo Hah! I am glad I decided against adding "obviously any counterexample would be some sort of monster group" in this post.
Nov 30, 2020 at 12:54 history answered YCor CC BY-SA 4.0