In this video, we look at two examples - in one Z_mxZ_n turns out to be a cyclic group and in the other it is not cyclic. We prove that the group Z_3xZ_4 of order 12 is cyclic by exhibiting atleast one element in it of order 12. We urge the viewer to prove that the group Z_2xZ_4 of order 8 is not cyclic by proving that it has no element of order 8. We conclude therefore that the direct product of cyclic groups need not be cyclic. We also raise the question as to what is the relation between m and n where the above group becomes cyclic.
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Негізгі бет Z_3xZ_4 is cyclic but Z_2xZ_4 is not cyclic - Chapter 11 - Lecture 5
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