Use with the (group-theory) tag. The tag "finite-groups" refers to questions asked in the field of Group Theory which, in particular, focus on the groups of finite order.

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How many Groups there are on a finite countable set?

Let say cardinality of set S is $n=|S|$. We know that there are $n^{n^2}$ all binary operations on that set. To find out how many groups can be created by this set and by those operations, we need not ...