Exercise
Consider the permutation group G = < a, b> where a = (1,2,3,4) and b = (1,3).
What is the order of G?
16
8
4
False,
the orbit of 1 equals {1,2,3,4}. The
the stabilizer of 1 can be generated by (2,4) and has order 2.
So ...
Correct, the orbit of 1 equals {1,2,3,4}. The
the stabilizer of 1 can be generated by (2,4) and has order 2.
So |G| = 4 · 2 = 8.
No, the subgroup generated by a has order 4, but does not contain b. Hence G has order at least 8.