Suppose H and K are distinct subgroups of a finite group G, and the orders of H and K are relatively prime, then prove H∩K={e}
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Pick $\displaystyle a \in H \cap K$ then if $\displaystyle ord(a)=b$ we have $\displaystyle b \vert \vert H \vert$ and $\displaystyle b \vert \vert K \vert$ so $\displaystyle b \vert (\vert H \vert , \vert K \vert )=1$ so...
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