when are relatively prime
Let and . Then the external direct product consists of elements , where and .
Next, we show that the group is cyclic. We do so by showing that it is generated by an element, namely : if generates , then for each , we must have for some . Such , if exists, would satisfy
The order of is , so is the order of . Since cyclic groups of the same order are isomorphic, we finally have .
|Title||when are relatively prime|
|Date of creation||2013-03-22 17:59:46|
|Last modified on||2013-03-22 17:59:46|
|Last modified by||yesitis (13730)|