Gemara

Chachamim use the "Vav" to teach that Asham Taluy must be worth at least two Shekalim, just like Asham Me'ilos.

R. Akiva holds that Ein Hekesh l'Mechtzah. (Each of these teaches about the other.)

Objection: This implies that Chachamim hold that Yesh Hekesh l'Mechtzah. This is not the Halachah! Rather, all agree that Ein Hekesh l'Mechtzah.

Gitin 64b (Mishnah): One can divorce a Na'arah Arusah (i.e. before Nisu'in) by giving the Get to her or to her father;

R. Yehudah says, we never find that each of two people has Reshus (jurisdiction) over one person. Rather, only her father can receive it.

65a (Rava): A girl at the age of Pa'utos (between six and 10, depending on her sharpness) can (receive her own Get and) become divorced, even if she was Mekudeshes mid'Oraisa by her father.

Kidushin 43b (Reish Lakish): Chachamim and R. Yehudah argue similarly about who can receive Kidushin for a Na'arah (only the father, or also herself);

(R. Yochanan): They argue only about divorce. All agree that only her father can receive her Kidushin.

(R. Yosi bar Chanina): R. Yochanan explains Chachamim as follows. When a girl is divorced, she returns herself to her father's Reshus, so (also) she can receive her own Get;

When she becomes Mekudeshes, she extracts herself from her father's Reshus, so only he can receive her Kidushin.

44a (R. Avin): Everyone in the Beis Midrash agreed with R. Yochanan. Reish Lakish was screaming 'Yatzah v'Haysah (a Hekesh equates Kidushin to divorce)', but no one heeded him.

44b (Rav Nachman): A Na'arah cannot make a Shali'ach to receive her Get.

Question (Mishnah): If a minor said 'receive my Get for me', she is not divorced until it reaches her hand.

Inference: If a Na'arah said this, she would be divorced when the Shali'ach gets it!

Answer: The case is, she has no father. (Therefore, she can make a Shali'ach.)

Rishonim

Rif (Gitin 30b): The Halachah follows Chachamim. Regarding Kidushin, all agree that her father receives it, but she cannot, for the Torah gave all Shevach Ne'urim (revenue that comes to a Na'arah) to her father. This is why Kidushin is different. Rava taught when a minor can receive her own Get, i.e. if her father died. In her father's lifetime, she is in his Reshus. Only he can receive the Get.

Rambam (Hilchos Gerushin 2:18): If a man was Mekadesh a minor through her father and divorced her when she is a minor, she is divorced when her father gets the Get.

Rashi (64b DH Hi): A Na'arah can receive her Get, for she is an adult. If she would be an orphan, she could be Mekadesh herself and receive her Get. Also now (that she has a father and cannot be Mekadesh herself), it is no different (regarding Get).

Rashi (43b DH Na'arah): The Tana'im argue about a Na'arah to teach the extremity of R. Yehudah, who holds that even a Na'arah cannot receive her own Get.

Note: This connotes that Chachamim hold that even a minor can receive her own Get. However, the next Rashi (DH Hi) says that she can receive her own Get 'because she is an adult.' Presumably this is why the Rosh (below) says that also here Rashi held that a minor cannot receive her own Get.

Rosh (Gitin 7:9) and Tosfos (64b DH Na'arah): Rashi here and in Kidushin wrote that a minor cannot receive her own Get. Also the Rif said so. Rashi later corrected himself there to say that she can receive her own Get. The Rivam proves this from Rav Nachman, who taught that a Na'arah cannot make a Shali'ach to receive her Get. The Gemara challenged him from a Mishnah that says that if a minor made a Shali'ach, she is not divorced until it reaches her hand, which implies that a Na'arah can make a Shali'ach. The Gemara answered that this is when she has no father. Initially, we thought that the Mishnah discusses a minor with a father, and even so she can receive her own Get! Since Rabanan argue about this, it is proper to be stringent.

Ran (Kidushin 18a DH Ba'a): Here Rashi says that also a minor can receive her own Get. Reish Lakish does not totally equate Kidushin to divorce, for surely a minor has no Da'as (understanding) to be Makneh herself (receive Kidushin). Rather, for a Na'arah they are the same. However, the Rif holds that a minor can receive her own Get only if her father died. We can dispel the proof from Rav Nachman. The questioner thought that the Mishnah discusses a girl with a father. The Gemara could have said 'the Mishnah holds that a minor can receive her own Get. You must admit that she has no father!' Sometimes the Gemara could have said 'you must admit...', but it does not. The Ramban says that Rava held that she is like an extra Yad (hand, i.e. power of acquisition) of her father, therefore a minor can receive her own Get, but we hold like Rav Nachman, that she is merely like a Shali'ach of her father, therefore a minor can receive it only with her father's consent. The simple reading of the Mishnah connotes that only a minor can receive her Get, but a Na'arah cannot. Do not say that the Mishnah taught a Na'arah to teach the extremity of R. Yehudah's opinion. If Chachamim hold that even a minor receives her own Get, it should have taught rather the extremity of their lenient opinion! The Ramban also supported the Rif from the Yerushalmi, which says that a minor Arusah cannot receive her own Get. Also Rav Hai Gaon says so.

Ran (Gitin 30a DH Masnisin): In Kidushin, Rashi says that a minor can receive her own Get. This is because even though a Na'arah is in her father's Reshus, she can receive her own Get. The same applies to a minor, as long as she has Da'as and can acquire for herself. (Note: he refers to Da'as of Pa'utos. All agree that a child is not considered a (proper) Bar Da'as until adulthood.)

Tosfos (Kidushin 44a DH Tzavach): Even though even Reish Lakish does not equate Kidushin to divorce, for a minor can receive her own Get, but she cannot receive her own Kidushin, in any case we must equate them as much as possible, for it says "v'Yatzah v'Haysah." If so, we equate Kidushin and divorce regarding a Na'arah. Granted, we must distinguish regarding a minor, for she has no Yad to accept Kidushin for herself, but she has a Yad to receive her Get once she had Nisu'in.

Pnei Yehoshua (64b DH uv'Hachi): Tosfos' question is not difficult. The Hekesh applies only to an adult. This is why Reish Lakish asked only about a Na'arah. R. Yochanan ignored the Hekesh, because there is reason to distinguish. Divorce returns her to her father's Reshus, but Kidushin removes her from her father's Reshus. When there is a reason to distinguish, we do not say that Ein Hekesh l'Mechtzah.

Poskim

Shulchan Aruch (EH 141:4): If a man was Mekadesh a minor through her father, and divorced her during Erusin in her father's lifetime, her father must receive the Get. She cannot receive it without his consent. Some say that she can receive her own Get.

Beis Yosef (DH ba'Meh): The Rif says that a minor Arusah with a father cannot get her own Get. The Ran, Ramban, Rav Hai Gaon, Rambam, Ra'avad, and Rashi in Gitin agree. Rashi in Kidushin says that she can receive her own Get. Tosfos says that this is primary, and the Ba'al ha'Ma'or, Ba'al ha'Itur, and Rosh agree. Since The Rif and Rambam agree, and several others hold like them, we rule like them. (However, when possible, one should be concerned for the opinion that disagrees.)

Bedek ha'Bayis: The last sentence should be deleted.

Note: The Beis Yosef did not retract because the other opinion is more lenient, so we need not be concerned for it. To consider her Safek divorced causes many stringencies, e.g. it forbids Yibum and marrying a Kohen, and if she accepted Kidushin from another man. Rather, we follow the first opinion even to be lenient. The Beis Yosef always rules like the majority of the Rif, Rambam and Rosh. The Beis Yosef initially wrote that surely the Rosh did not write 'since Rabanan argue about this, it is proper to be stringent'. I.e. the Rosh had no Safek; he accepted the Rivam's proof. In Bedek ha'Bayis he retracted, for the Rosh in Gitin explicitly says so, i.e. the Rosh was unsure. Since the Rosh does not Vadai oppose the Rif and Rambam, the Beis Yosef totally relies on them. In the Shulchan Aruch, he mentioned the other opinion (but did not say to be concerned for it). Many say that he wrote the Shulchan Aruch after Bedek ha'Bayis (Yad Malachi citing Keneses ha'Gedolah and Ginas Veradim OC 4:9), but the Chida questioned this (Shem ha'Gedolim, Sofrim, Os Shin, 75).

Beis Shmuel (6): Since the Mechaber favors the opinion that a minor cannot receive her own Get, this shows that she has no Yad, and she cannot acquire through her Chatzer. The Rema (CM 243:23) rules like this. However, in Seder ha'Get (after Siman 154, 94) the Mechaber connotes that the opinion that she can receive her own Get is primary. (It says 'it is proper to be stringent and receive it only through her father.')

Gra (15): If her father agrees, this works even for Kidushin (even for a minor - Kidushin 19a), even though we hold like R. Yochanan, that all agree that even a Na'arah cannot receive her own Kidushin.