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Oct 10, 2023 at 13:53 vote accept CommunityBot
Oct 10, 2023 at 11:03 comment added YCor To be explicit, the simplest example seems to be the inclusion $U(F_1)\subseteq U(F_2)$ with $F_2$ the symmetric group on 3 elements, and $F_1$ cyclic of order 2, i.e., generated by a transposition.
Oct 10, 2023 at 9:19 comment added Tom De Medts @YCor Thanks, I have modified the definition of $G$ (this is indeed what I meant to say).
Oct 10, 2023 at 9:17 history edited Tom De Medts CC BY-SA 4.0
added 27 characters in body
Oct 10, 2023 at 9:10 comment added YCor Your definition of $G$ is strange because many elements of the coset $\mathrm{Aut}(G)\smallsetminus T$ have no inversion (e.g., a translation of odd length). $G$ is just the group of elements mapping one/every vertex to even distance.
Oct 10, 2023 at 8:36 history answered Tom De Medts CC BY-SA 4.0