NOTES ON SYLOW’S THEOREMS
NOTES ON SYLOW’S THEOREMS 5 group. This means every element of Qmaps to the identity element of N G(P m)=P m. In other words, for all x 2Q; xP m = P m, which is equivalent to x2P m. Therefore, Q P m. But these are both Sylow p-subgroups so they’re both of order p , so Qis equal to P m. This shows that after all, Qis in S.
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