Show that the order of the group of automorphism of a finite group of order n is a divisor of n !.
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Show that the order of the group of
automorphism of a finite group of
order n is a divisor of n !.
Step by step
Solved in 3 steps
- Show that every subgroup of an abelian group is normal.27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.9. Let be a group of all nonzero real numbers under multiplication. Find a subset of that is closed under multiplication but is not a subgroup of .