Some thoughts and experiments on Bergman's compact amalgamation problem

Abstract

We study the question whether copies of $S^1$ in $\mathrm{SU}(3)$ can be amalgamated in a compact group. This is the simplest instance of a fundamental open problem in the theory of compact groups raised by George Bergman in 1987. Considerable computational experiments suggest that the answer is positive in this case. We obtain a positive answer for a relaxed problem using theoretical considerations.

15 pages, 2 figures, 3 tables; update contains minor changes that address referee comments