TITLE: Does the symmetric group on an infinite set have a minimal generating set?
QUESTION [29 upvotes]: To clarify the terms in the question above:
The symmetric group Sym($\Omega$) on a set $\Omega$ consists of all bijections from $\Omega$ to $\Omega$ under composition of functions. A generating set $X \subseteq \Omega$ is minimal if no proper subset of $X$ generates Sym($\Omega$).
This might be a difficult question, but perhaps the answer is known already?

REPLY [4 votes]: The canonical paper on the subject (don't be fooled by the publication date, it had been around for years before then) is George Bergman's gem:
Bergman, George M., Generating infinite symmetric groups., Bull. Lond. Math. Soc. 38, No. 3, 429-440 (2006). ZBL1103.20003.