Intersection of cyclic subgroups

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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