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hi! i am new in abstract algebra.
how can i prove that a group of order 5 is Abelian?
thanks in advance.
how can i prove that a group of order 5 is Abelian?
thanks in advance.
The above is known as Lagrange's theorem. It's fundamental to group theory. When I was studying group theory, I learnt it before I knew the defintion of "cyclic". You really won't be able to go far without the theorem so I suggest you look up the theorem. Any text book on goup theory will have it. The proof is not hard, but envolves the concept of cosets. Have you met that yet??philosophking said:"The order of a subgroup must divide the order of the group"--what if one hasn't seen that before, is there an easy proof, besides the psuedo-method i proposed?