Notoriously is a word used to describe a person, thing, or action that is well known for being bad or unpleasant. There are several synonyms for notoriously, including infamously, notoriously, and widely. Infamously is used to describe some action or event that has caused a great deal of negative publicity or shame. Widely is used to describe actions, events or occurrences that are widely recognized or known. Other synonyms for notorious include disreputably, scandalously, and disgracefully. Choosing the right synonym for notoriously depends on the context of the sentence and what the author is trying to convey.