Definition
Alternating group A_1
Even permutations of one letter under composition.
The alternating group consists of the even permutations of , with composition as multiplication. The unique permutation has sign , so this extends the convention to one letter.
Order and simplicity
Its order is . There is only the identity; the trivial group is not simple.
References
- J. S. Milne, Group Theory, v4.01, §4, symmetric and alternating groups; Theorem 4.33 and Remark 4.34, p. 69.