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10 Courses/01 - WiSe 2025_26/DAS/Groups.md Normal file
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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