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The decree was then rendered that he should be burnt and his wife be slain.

The Gemara explains the cause for their punishments: The punishment of being burnt came upon him because he pronounced the Holy name of G-d in its full spelling in public.  His wife was punished by being slain because she did not prevent him from doing it. From this it was deduced that anyone who has the power to prevent one from doing wrong and does not prevent it, is punished for him.