Abusive is a related term of infamous.
In archaic|lang=en terms the difference between abusive and infamous
is that
abusive is (archaic) given to misusing; also, full of abuses while
infamous is (archaic) in england / great britain, a judicial punishment which deprived the infamous person of certain rights; this included a prohibition against holding public office, exercising the franchise, receiving a public pension, serving on a jury, or giving testimony in a court of law.
As adjectives the difference between abusive and infamous
is that
abusive is wrongly used; perverted; misapplied; unjust; illegal while
infamous is having a bad reputation, disreputable; of bad report; notoriously vile; detestable; widely known, especially for something bad.