Exercise
The element g = (1,2)(3,4,5)(6,7,8,9,10) generates a subgroup of S10 isomorphic to:
Z
Z/10Z
Z/30Z
No, the group is finite.
No, g10 = (3,4,5).
Yes.
Exercise
The element g = (1,2)(3,4,5)(6,7,8,9,10) generates a subgroup of S10 isomorphic to:
Z
Z/10Z
Z/30Z