uni_notes/Studium/DAS/Groups.md

Groups are Closures that have the following properties:

1. closure: Every element which is a result of the binary operation of the group is part of the group
2. associativity: changing the order of operations doesn't change the result
3. identity: there is a neutral element (0 in addition, 1 in multiplication)
4. inverses: every element has a element when combined results in the identity element (+5 + (-5) = 0)

Order of elements in a cyclic group

"order"(a) = n/("gcd(a,n)") n: from ZZ\/10ZZ => 10 a: element to find order of