Question

constructions of finite symmetric group in Algebra​

Answer 1

Step-by-step explanation:

the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group {\displaystyle S_{n}}S_{n} defined over a finite set of {\displaystyle n}n symbols consists of the permutations that can be performed on the {\displaystyle n}n symbols.[1] Since there are {\displaystyle n!}n! ({\displaystyle n}n factorial) such permutation operations, the order (number of elements) of the symmetric group {\displaystyle S_{n}}S_{n} is {\displaystyle n!}n!.

Answer 2

Answer:

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