In 3 Nephi 5:12 we find the following:
And behold, I am called Mormon, being called after the land of Mormon, the land in which Alma did establish the church among the people, yea, the first church which was established among them after their transgression. (emphasis added)
According to Rodney Turner, the phrase "after their transgression" refers to the apostasy in the time of Mosiah I, which led to the destruction of the first Nephite nation (Jacob 3:4, Jarom 1:10; Omni 1:12), rather than that of King Noah and his supporters as described in Zeniff's record (Mosiah 9-22). In any case, had there been a functioning church of Christ in the land of Zarahemla, there would have been no need for Alma to organize a second church, nor for Mosiah to grant Alma permission to set up branches throughout that land. In addressing the Nephites in Zarahemla, Alma said: "We were brought into this land, and here we began to establish the church of God throughout this land also." (Alma 5:5; italics added) [Rodney Turner, "Two Prophets: Abinadi and Alma," in Studies in Scripture: Book of Mormon, Part 1, p. 255, 259]
Note* It seems to me that the "transgression" was three-fold and progressive. In the land of Nephi, the Nephites were governed by a "Church-State" authority resting with the king. Apparently there became sufficient numbers of non-believers ("Lamanites" or "dissenters") that brought the downfall of this type of government. Mosiah fled to the land of Zarahemla and established a righteous Nephite kingship, however the population continued to be predominantly Mulekite non-believers. Zeniff returned to the land of Nephi to re-establish a righteous Nephite kingship, yet from his over-zealous efforts sprang an "church-state" rule directed by an unrighteous king. Thus it seems that no matter which way they turned for relief, the Nephites couldn't find a solution to re-establish the righteous Nephite kingship rule of both church and state that had been lost through the "transgression" of the Nephites in general, and the "Nephite" King Noah in particular. Could this "transgression" in some way be related to the words of Mosiah II found in Mosiah 29:25-27) that if ever non-believers numbered more than believers it would lead to destruction? And how could he say that with so many of the people of Zarahemla (Mulekites) among the crowd? "Now there were not so many of the children of Nephi . . . as there were of the people of Zarahemla, who was a descendant of Mulek" (Mosiah 25:2) [Alan C. Miner, Personal Notes]