The AMA, one of many professional groups, like to control its own doctors. Everyone, including the Brady family and the Gilligan's Island crew members, have a t.v. show. The beating of their hearts set their eyes aglow. Sally, Sue, Jim and Joe-Bob, all members of the fraternity, eats at McDonalds. The swimming of the Olympic teams, something millions of people watched, were over-rated.
Pronouns refer to the nearest noun of the same number.
If it's singular, then the antecedent is singular. If it's plural, then the antecendent is plural. Match the antecedent to its pronoun. Each reader has their own ideas about what makes good writing. Each reader has his or her own ideas about what makes good writing.