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Give an example to show that a direct product of two cyclic groups is not necessarily
Chapter 15, Problem 15.19(choose chapter or problem)
QUESTION:
Give an example to show that a direct product of two cyclic groups is not necessarily cyclic. (Compare 15.18.)
Questions & Answers
QUESTION:
Give an example to show that a direct product of two cyclic groups is not necessarily cyclic. (Compare 15.18.)
ANSWER:Step 1 of 4
In general, products of cyclic groups are not cyclic. If is the cyclic group of order is not cyclic.
The direct product of two cyclic groups, is cyclic if and only if the
(where is the order of one of the cycle groups, and the order of the others.)
Note, we must have a Direct product of order .