Abstract Algebra | Direct product of groups.

We determine when the direct product of cyclic groups is cyclic.

[jasonthomas]

I can understand this, until the <= implication, where you say that the |1| = m. What is 1 in this case? Is this the element in Z_m? Thanks for the video.

[하정훈-jj]

11:13. Here, are we saying that "Zm X Zn has to have order of mn or multiple of mn, but since the (a, b) has to be a generator as was shown above, |(a, b)| has to be greater or equal to mn. Thus, it's a contraction to (a, b)<mn?" Not sure if I'm understanding this part correctly,

[saravanakumark]

Is that property "Cross product of two cyclic group is cyclic iff gcd(m, n)=1" true for more than two cyclic groups ?

[punditgi]

Can you clean the blackboard first?
Otherwise, great info! 😊