Definition
Alternating group A_8
Even permutations of 8 letters under composition.
The alternating group consists of the even permutations of , with composition as multiplication.
Order and simplicity
Its order is . It is nonabelian simple, as holds for alternating groups of every degree at least five.
References
- J. S. Milne, Group Theory, v4.01, §4, symmetric and alternating groups; Theorem 4.33 and Remark 4.34, p. 69.