according to rabbah he holds that one can't have pieces from the lulav but the mishna on 36b says the same species is mutar. can rabbah argue with a mishanh?
1) Rabah on 37a is not discussing pieces from the Lulav. Even though he states that "Lekichah Tamah" (a "complete taking") is required, in this case this does not refer to pieces of Lulav, but rather he means that if one holds the Lulav using something else this is not considered a "complete taking" of the Lulav. Therefore, according to Rabah one may not hold the Lulav using a cloth.
The Mishnah on 36b is discussing something different. When one ties the species (the Lulav, Aravos, and Hadasim) together, do they have to be tied with one of the species? Rebbi Yehudah maintains that they must, while Rebbi Meir maintains that this is not necessary, and one may even tie them together with string. The Halachah follows Rebbi Meir, which is presumably how Rabah rules.
2) Rabah cannot argue with a Mishnah. The Gemara in Kesuvos (8a) states that Rav was a Tana and could argue with the Mishnah. However, Tosfos there (DH Rav) writes that Rebbi Yochanan is not a Tana and therefore may not argue with the Mishnah. Rabah was later than Rebbi Yochanan and certainly could not argue with the Mishnah.
Kol Tuv,
Dovid Bloom
not 37a , 37b when they la'Dutz and according to artsscroll its the hadasim and aravos la'Gutz.
1) Rabah states (concerning la'Dutz) that when the Lulav is forced into the bundle this causes the leaves of the Hadas and Aravah to fall off (note that this is said concerning la'Dutz, not concerning la'Guz). The Rashash explains that the problem is that the leaves that fall off are no longer part of the Mitzvah. Even though the Mishnah (36b) states that everyone agrees that the same species does not constitute a Chatzitzah, this is only when it is part of the Mitzvah, but since the leaves that fall off are not part of the Mitzvah they constitute a Chatzitzah between the different parts.
2) The Avnei Nezer (Orach Chaim 492:4) explains that even though the Halachah is that "Eged" (tying together the three species) is only a way of doing the Mitzvah in the choicest manner, but the Lulav is valid even if they are not joined together, this refers only to the "Eged" achieved by tying them together. In contrast, "Eged Yad" (the requirement that the three species be held in one hand) is crucial and if one does not hold them in one hand, the Mitzvah is not valid even b'Di'eved. If there are other irrelevant pieces in the bundle apart from the pieces of the Mitzvah, this means that the three species are considered as not being in the same hand, and according to Rabah this is Pasul.
Kol Tuv,
Dovid Bloom