Brant Gardner comments, How is it that these two peoples (of Mosiah and of Zarahemla) get to know so much about each others genealogy so quickly? Why is it so important for Zarahemla to give "a genealogy of his fathers" (Omni 1:18)? And why does Amaleki mention this fact just before noting that the two groups united? It has to do with the principle of kin interactions. John Sorenson notes that a Mayan practice at the time of the Spanish conquest shows the same principle governing how to get along in strange territory: "When anyone finds himself in a strange region and in need, he has recourse to those of his name [kin group]; and if there are any, they receive him and treat him with all kindness."
It is therefore quite understandable that one of the first "orders of business" with the newcomers straggling in out of the wilderness would be to examine genealogies to see if there were any kinship obligations between them. What they found was not only a kinship, but one of utmost importance as the tie returned to the origins of both groups in Jerusalem, which by now must have been nearly the stuff of legend and myth. Having thus established an important bond linking them both to a common sacred origin, the ties of kinship took over, they "did rejoice exceedingly" (Omni 1:14), and eventually "did unite together" (Omni 1:19) [Brant Gardner, "Book of Mormon Commentary," [http://www.highfiber.com/~nahualli/LDStopics/Omni/] Omni1.htm, p. 24]