Thread: Question related to field

Why can't a field have exactly 6 elements? I tried to go over the axioms but couldn't figure out anything. Help please

The number of elements in a finite field must be , where p is a prime and k is a positive integer. 6 is not of the form .

Originally Posted by namelessguy

Why can't a field have exactly 6 elements? I tried to go over the axioms but couldn't figure out anything. Help please

We can make it even easier than Jane Bennet said. It can be easily proven* that the characteristic of a field (in fact an integral domain) must be or (a prime).



*)Define as .