Cyclic Groups - Is it a Cyclyc group?

, while Z is the integers (I believe the action should be '+' for it to be a group, otherwise, for instance in multiplication, (0,0) has no inverse element).

How do I generally check whether it's a cyclic group? It has 150 elements (Surprised)

Thanks (Happy)

Quote:

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Originally Posted by adam63

, while Z is the integers (I believe the action should be '+' for it to be a group, otherwise, for instance in multiplication, (0,0) has no inverse element).

How do I generally check whether it's a cyclic group? It has 150 elements (Surprised)

Thanks (Happy)

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You need to find a generator. However, this group is NOT a cyclic group.

Assume generates your group. Then for all (why?). However, take ...

Something to think about: Why does this work? Why the number 30?

Nice, gcd(10,15)=30.
And, since (a,b) is the generator, then |(a,b)|=150.

Got it :) ! Thank you very much!

Quote:

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Originally Posted by adam63

Nice, gcd(10,15)=30.
And, since (a,b) is the generator, then |(a,b)|=150.

Got it :) ! Thank you very much!

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lcm, not gcd...but yeah. Can you see the generalisation? It is a neat theorem, and one to remember...