Let be a group with normal subgroups and .

Let .

Suppose $M \cap \langle a \rangle =1$ and $N \cap \langle a \rangle= \langle a^{s} \rangle$ for some positive integer .

Can we find $MN \cap \langle a \rangle$???

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- September 19th 2011, 11:09 PMdeniselim17intersections of subgroups
Let be a group with normal subgroups and .

Let .

Suppose $M \cap \langle a \rangle =1$ and $N \cap \langle a \rangle= \langle a^{s} \rangle$ for some positive integer .

Can we find $MN \cap \langle a \rangle$??? - September 19th 2011, 11:18 PMDrexel28Re: intersections of subgroups
- September 20th 2011, 02:21 AMSwlabrRe: intersections of subgroups
I am not entirely sure what you are asking...I mean, given finite time of course you can! On the other hand, there isn't a definitive answer. For example, take,

( denoting the cyclic group of order ), with your elements being of the form with . Now, let . Clearly, if then , while if then . Clearly, . On the other hand, if we let then contains but still...so, basically, it depends on and and , and can be very different depending on different choices...