Synonyms for the term "serve abjectly" would include words such as grovel, kowtow, bow, scrape, fawn, and submit. Each term is used to describe a type of subservient behavior where an individual seeks to please another person or group at the expense of their own dignity or self-respect. The term "serve abjectly" is often used in reference to relationships where one person has a higher status or position of power than the other. In such cases, the person serving abjectly may feel compelled to act in a certain way to maintain their status or avoid punishment or retribution.