There are 16 possible binary operations on a set of 2 elements. How many of these give a structure of a group?

According the following problem: Let S be a set having exactly one element. How many different binary operations can be defined on S? Answer the question if S has exactly 2 elements exactly 3 elements exactly n elements. there are 16 possible binary operations on a set of 2 elements. How many of these give a... show more According the following problem:
Let S be a set having exactly one element. How many different binary operations can be defined on S? Answer the question if S has exactly 2 elements exactly 3 elements exactly n elements.
there are 16 possible binary operations on a set of 2 elements. How many of these give a structure of a group? How many of the 19,683 possible binary operations on a set of 3 elements give a group structure.
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