I'm sorry...I am still getting no where...
I do appreciate everyone's help, though. I will report if I make any progress. Going to talk to the professor tomorrow...this is so discouraging...
If x is of order p, there are p distinct elements of powers of x...right? <x> will have order p also. one of those will be e, so p-1 of them can have order p.
Z5 has 4 elements with order 5.
thinking...
sorry, I am usually not so dense..
I am sorry, I am still stuck. If x has order p, then x inverse must also have order p, and must also be in the group. then that is 2 elements...unless x is it's own inverse. So I think I am totally missing something here? HELP!
Thank you...
Homework Statement
Suppose a finite group has exactly n elements of order p where p is prime. Prove that either n=0 or p divides n + 1.
Homework Equations
My professor says that this proof is similar to the proof of Lagrange's Theorem, in our Abstract Algebra book (Gallian).
The...