proof that all cyclic groups of the same order are isomorphic to each other
Note that .
If is finite, then let . Thus, . If , then divides . Therefore, . By the first isomorphism theorem, .
Let and be cyclic groups of the same order. If and are infinite, then, by the above , and . If and are finite of order , then, by the above , and . In any case, it follows that . ∎
|Title||proof that all cyclic groups of the same order are isomorphic to each other|
|Date of creation||2013-03-22 13:30:41|
|Last modified on||2013-03-22 13:30:41|
|Last modified by||Wkbj79 (1863)|