Definition
Symmetric group S_1
Permutations of one letter under composition.
The symmetric group is the group of all bijections of , with composition as multiplication.
Order and normal subgroup
There are 1 permutations: choose the images of the 1 letters successively. This group is trivial and hence not simple.
References
- J. S. Milne, Group Theory, v4.01, §4, symmetric and alternating groups; Theorem 4.33 and Remark 4.34, p. 69.