A pressing question:

If we are given two cyclic groups, and we take a cartesian product of the two, is the result also a cyclic group?

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- Nov 15th 2009, 06:02 PMflabbergastedmanCartesian product and cyclic groups
A pressing question:

If we are given two cyclic groups, and we take a cartesian product of the two, is the result also a cyclic group? - Nov 15th 2009, 06:32 PMJose27
is a group of order 4 where all it's elements have order 2

- Nov 15th 2009, 08:06 PMflabbergastedman
Excellent! Thank you very much

- Nov 16th 2009, 09:03 AMDrexel28
In fact, is cyclic iff . To think of why this is we need some element of to be of exactly order but it is clear the order of is . Therefore lastly noting that we conclude that . And since all cyclic groups of order are isomorphic to this is the case for any cyclic groups.

- Nov 16th 2009, 03:34 PMflabbergastedman
- Nov 16th 2009, 03:47 PMDrexel28