Number of Elements of Order 4
True of false - for any group G, the number of elements x belongs to G such that x^4 = e is at most 4.
I found on another forum the following solution but many steps were skipped...
"Clearly e^4 = e.
x^5 is an element such that (x^5)^4 = e.
So are x^10 and x^15.
But these are just 4 elements.
So clearly there is no counterexample with a cyclic group.
Now you try examples with non-cyclic Abelian groups, and Non-Abelian groups and see what you come up with..."
what actually is C_20??and i cant think of an example of any non-cyclic abelian groups :( can anyone please talk me through where is method is going, preferably step by step??thanksss