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}|

by Isomorphizm June 17, 2020

by Ms Lafond November 13, 2019

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.

by qsqazxcvfrew March 29, 2018

When someone glares at madie but actually doesn't and alyssa,haylie, Anika, and mallorie all hated her but she's not brave enough to ask

by Rosehaters🍓 September 13, 2017

A small selection of people. Generally named Alyssa, Haylie, Anika, and Mallorie! That Madie claims glares at them all the time! She also claims that Alyssa hates her without actually asking Alyssa before making the assumption.

by Rosehaters🍓 September 13, 2017

a group of 23 exceedingly cool individuals who can often be found loitering in various places for entertainment purposes. often mistaken as being "too sophisticated" or "too innocent" by other groups, The Group is in fact the best group to have around when one wants to have fun, and due to all of the brilliant personalities within The Group, there is never a dull moment.

'wow... who are those 23 incredibly cool people having so much sophisticated fun over there?'

'dude.... thats The Group.... Duh..'

'omg! look at those people loitering outside Johnstons Court... they are so trying to be The Group..'

'i always feel so lonely when i delete myself from The Group..'

'dude.... thats The Group.... Duh..'

'omg! look at those people loitering outside Johnstons Court... they are so trying to be The Group..'

'i always feel so lonely when i delete myself from The Group..'

by bond.jamesbond. August 23, 2011

by moneylongproductions July 7, 2014