What is the legality of owning an alligator as a pet in the United States?

26 states outright forbid owning an alligator as a pet. 12 states allow ownership with proper permitting. 11 states allow ownership with no need for a permit; of those 11 states, 5 do not have any permit requirements to own any exotic animal. While Wyoming prohibits certain game animals from being owned as pets, the state does not include nor exclude alligators in specific listings, so presumably, one can own a pet alligator unpermitted in Wyoming.