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Questions about the branch of algebra that deals with groups.

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For the symmetric group on an infinite set, is there a generating set of strictly smaller ca... [closed]

Let $S_{\kappa}$ denote the symmetric group on some set of cardinality $\kappa$. Does there exist a generating set $X \subset S_{\kappa}$ such that $|X| < |S_{\kappa}|$ ($\stackrel{?}{=} 2^{\kappa} …
Felix Denis's user avatar