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※ 引述《kcir ()》之銘言：
: 請問有人知道怎麼證明
: "If the order of a group is a prime, then it is cyclic."
: 嗎?
G is a gruop.
|G| = p>=2
pick aεG\{e} where e is the identity.
claim <a> = G
pf. If <a>!=G
By Lagrange's Thm, |<a>| | p => |<a>| = 1
then <a> = {e} ,contradiction.
then G is cyclic
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