Short Answer
Depends on which domain of discourse you are asking about: philosophical logic or legal logic since they might not align. We'll examine both.
Long Answer
¡Bienvenidos! You have several domains of discourse here imposed over logical ruminations including history, political science, and law. I would rewrite the argument differently, since the argumentation is an intersection of logic and political law, and your equivalent argument has been stripped of the legal premise.
P1: Spain did not assimilate the slave oligarchy. (true historical claim)
P2: Santo Domingo was part of Spain. (true political claim)
P3: According to the logic of law, a tributary cannot entail the political systems that the suzerain does not entail. (a legal claim predicated upon the legal system)
Conclusion: Santo Domingo could not assimilate the slave oligarchy as a political system.
So, the crux of the matter is that one has to draw a distinction between philosophical logic and legal logic because the two don't always agree. While triers of fact aspire to implement logic legally, they are often constrained philosophically, such as in the case of stare decisis in Anglo-English legal traditions. Thus, the question of whether or not the argument is fallacious can be answered in two ways, philosophically and legally. So let's do each.
Logically
Absolutely, in philosophical logic both the fallacy of division and fallacy of composition are fallacies and making an argument predicated upon them is specious. To insist that something is true of a part because of it is true of a whole based on the rationale that there is a metaphysical necessity involved regarding properties is bad logic.
Legally
The law isn't strictly logical in the philosophical sense, because legal arguments generally start from positions that may be unvetted, nonsensical, contradictory, or even silly. For instance, the state of Indiana in the US once passed a law attempting to legislate the value of Pi. Under the American judicial system, a judge is generally constrained by stare decisis or by laws passed by a representational body a concept in US law known as judicial review and enshrined under constitutional law in Marbury v. Madison. So, if the US Congress passes a law that embodies the fallacy of division for political and economic law, case law is established accepting the premise, then the generally only the US Supreme Court has the power to deem the law null and void, and then within the context of the apparatus of US Constitution case law. So, it is possible to consider the argument rewritten as not only legally logical, but then binding upon the parties of the litigation.
Conclusion
One can see the philosophical fallacy involved, but it is important to draw the distinction between philosophical and legal reasoning. This important distinction is one drawn by the philosophy of logic itself which recognizes various distinctions in logic such as formal logic, informal logic, common sense reasoning, defeasible logic, etc.
EDIT
Here's my translation as a native English speaker:
As the reader will see, Santo Domingo came close to forming a slavery-based, sugar-industrial oligarchy in the first half of the sixteenth century; but Santo Domingo was part of Spain, and logically, in one part one cannot grow or come to what the whole was not able to take in. So, the origin of our shortcomings -- that it is in the failure of that effort made in the sixteenth century -- one finds a distant deficiency whose roots were not even in Spain in 1492, but rather further back; and in the last instance they went back and are systemic shortcomings neither of Spain nor the Dominican people. Furthermore, this book limits itself to depict, and to try to interpret, the Dominican social composition, not the Spanish one, therefore its conclusions should be regarded with respect to Santo Domingo, not to Spain. From the same book, one comes away with that the Dominican people cannot have hopes of knowing a better future than the past if they don't start to change the system in which they have seen failing for nearly five hundred years. To prove that that system doesn't work in Santo Domingo, five centuries is more than enough.
So, it depends on what the author is referring to. There ARE contexts where parts and wholes relate in such a way that it is not fallacy to impute properties of the whole to the part, such as in the transitivity of space. For instance, if a whole gallon container cannot contain the milk, one quarter of a gallon cannot either. Or legally, if federal law prohibits an activity, than a state subject to the federal law also must enforce the prohibition of the activity. If the author stated that Spain passed a law outlawing such oligarchies, then Santo Domingo would be required to enforce that law same as Spain. But the word 'asimilar' seems to suggest something broader than a legal ruling, like a cultural inability, that el pueblo de Espana for some reason rejected it. In that case, there's no reason the upper class of Santo Domingo couldn't have embraced social institutions that those of Spain rejected. If you provide the prior paragraph, I might be able to confirm.
