infamously comes from infamous + -ly, from Latin infamis ('of ill repute'), from in- ('not') + fama ('fame, report'), from fari ('to speak'). Morphologically, the ending is part of the etymology: the suffix is attached to the older base named in the history, producing a later English derivative. In present English, the adverb sense is "in a way that is well known for being bad or wicked", so the historical development ends in a clearly identifiable modern dictionary use. The same base also appears in related forms such as infamous, infamy, fame, and famous. Its semantic neighborhood includes notoriously, disreputably, scandalously, and shamefully, which helps locate the modern sense without adding a separate etymological claim. The named historical forms include Latin infamis and Latin fama.