Cyclic Group,Permutation Group
Group generated by a single element a
Example: Group described as ka, where k is an entire number.
- Z: set of entire numbers
- -> Additive group
- nZ: set of multiples of n
- -> Subgroup of Z
- Quotient group
- -> Finite cyclic group
Infinite cyclic group
ZFinite cyclic group
Finite cyclic group's n: order (period)
n-th order symmetric group
:All permutations of n finite sets
Transposition:
Only two elements
of 
are exchanged. 
The elements of
can be expressed as products of transpositions.Cyclic permutation:
The remaining elements of
are fixed.
The elements of
can be expressed as products of coprime cyclic permutations.[0]Top