21.11 (2026)

Can some or all groups of the following sorts be written as homomorphic images of nonprincipal ultraproducts of countable families of groups? This is Question 18 in (G. M. Bergman, Pacific J. Math., 274 (2015) 451–495).
$\qquad$ (a) Infinite finitely generated groups of finite exponent.
$\qquad$ (b) For an infinite set $X$, the group of those permutations of $X$ that move only finitely many elements.
It is known that no group of permutations containing an element with exactly one infinite orbit can be written as an image of such an ultraproduct (ibid.).