11 lines
566 B
Markdown
11 lines
566 B
Markdown
Groups are Closures that have the following properties:
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1. **closure**: Every element which is a result of the binary operation of the group is part of the group
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2. **associativity**: changing the order of operations doesn't change the result
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3. **identity**: there is a neutral element ($0$ in addition, $1$ in multiplication)
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4. **inverses**: every element has a element when combined results in the identity element ($+5 + (-5) = 0$)
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## Order of elements in a cyclic group
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$"order"(a) = n/("gcd(a,n)")$
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$n$: from $ZZ\/10ZZ$ => $10$
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$a$: element to find order of |