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.
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}|
k divides |G| => k divides |{g∈ G : g^k = e}|
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Get the group mug.The group of skinny bitches who are always popular and you hate them while aspiring to be them. Then, 10 years later they are all meth heads or fat. Mainly meth heads. And by mainly I mean all of them.
Girl: Remember "That Group"?
Guy: Yeah I remember, you know they all got arrested for crack??
Girl: Doesn't surprise me.
Guy: Yeah I remember, you know they all got arrested for crack??
Girl: Doesn't surprise me.
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Get the groupe mug.Abstract Algebra: If G is a nonmpty set that is equipped with a binary relation * that satisfies the following axioms:
1. Closure
2. Associativity
3. There is an element e in G s.t. a*e=a=e*a for all a in G
4. For each a in G, there is an element d in G such that a*d=e and d*a=e
Then G is a group under the operation *
1. Closure
2. Associativity
3. There is an element e in G s.t. a*e=a=e*a for all a in G
4. For each a in G, there is an element d in G such that a*d=e and d*a=e
Then G is a group under the operation *
The set of integers is a group under addition.
The set of permutations in S_n is a group under composition.
The subset from the complex numbers {1, -1, i, -1} is a group under multiplication.
The set of permutations in S_n is a group under composition.
The subset from the complex numbers {1, -1, i, -1} is a group under multiplication.
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