The mitzvah to recite Hallel that Chazal instituted regarding Chanukah was in fact a direct result of the miracle of Chanukah; however, its essence is not to publicize the miracle but rather to give thanks for the miracle. On the other hand, the mitzvah of lighting candles was instituted in order to publicize the miracle. Therefore we can apply the rule of af ha’eim hayu b’osah haness – thereby obligating women in the mitzvah of lighting candles but not in the mitzvah of saying Hallel on Chanukah.
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