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fk378
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Homework Statement
Let G be a group and let H,K be subgroups of G.
Assume that G is finite and that the indices |G
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
Hint: Show that |G
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
The Attempt at a Solution
First off, why do the indices have to be relatively prime?
I don't know how to show that |G
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
EDIT:
Is the intersection of the left coset of H and the left coset of K disjoint? Since they are both equivalence classes they would have to either be disjoint or equal, no? So then |G
![Gah! :H :H](/styles/physicsforums/xenforo/smilies/arghh.png)
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