Intersection of cyclic subgroups

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    Cyclic Intersection
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SUMMARY

The intersection of two cyclic subgroups H1 and H2 of a finite order group G is indeed a cyclic subgroup of G. This conclusion is based on the property that all subgroups of cyclic groups are cyclic. Therefore, if H1 and H2 are cyclic, their intersection will also be cyclic. Additionally, the generators of the intersection can be determined from the generators of H1 and H2.

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Chen
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This time I need a yes/no answer (but a definitive one!):
Suppose we have a group of finite order G, and two cyclic subgroups of G named H1 and H2. I know the intersection of H1 and H2 is also a subground of G, question is - is it also cyclic? And can I tell who is the creator of it, suppose I have the creators of H1 and H2?

Thanks,
Chen
 
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Cyclic is easy. The intersection of H1 and H2 is a subgroup of H1. Subgroups of cyclic groups are cyclic.
 
Thank you. :smile:
 

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