Joe likes to go fishing. He knows that stronger the fishing line is, the larger the fish that he can catch

Mathematics

2 answers:

den301095 [7]3 years ago

6 0

he can catch stronger fish

Tomtit [17]3 years ago

5 0

Im guessing this is a True or False question, if so then it is True.

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$\Rightarrow$

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$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .