According to Peter Cameron (in his "Notes On Classical Groups", available on his webpage) "Paul Cohn constructed an example of a division ring $F$ such that all elements of $F\backslash\{0,1\}$ are conjugate in the multiplicative group of F." This in particular implies that the group can be chosen to be the multiplicative group of a division ring.
Name
- 2k
- 14
- 21