Group

The Chad of all algebraic structures, a group is a set equipped with an associative binary operation, which contains an identity as well as an inverse for each element.

Groups give mathematicians a general way of describing structures with symmetry. They are very sexy and I dream about them in my sleep.

If (G, • ) is a group with identity e, then Frobenius’ Theorem tells us that:
k divides |G| => k divides |{g∈ G : g^k = e}|

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