Argument

The usual rule when adding the suffix –ment to verbs ending in <e> is that the <e> is retained; this is what we find in words like placement, movement, achievement.  However, argument differs in dropping the <e>.  Because of this, arguement is a common misspelling of this word, one which some people think should be accepted as a valid alternative.  The website arguement.net deliberately adopts the misspelling, defending its choice on the grounds that misspellings like this are ‘so benign that usually they serve only as a criticizing point for people who can't argue arguments, but are switching their focus to these “fundamental” flaws in your character’. 

There is also an emerging view that arguement is a legitimate alternative in British English, similar to the case of judgement and judgment, where both spellings are acceptable.  Urban Dictionary defines arguement as: ‘The alternate spelling of the word argument in British English’.  A similar view was offered on Yahoo answers in a discussion prompted by a user’s request for the correct spelling of argument, in which one respondent claimed that argument is American usage and arguement the correct British spelling.  This answer was contradicted by the subsequent reply, which identified the correct spelling, but for the wrong reason: ‘When you add a suffix to a word that has an e at the end you almost always drop the e’.  All of which goes to show that if you want the correct spelling of a word, it’s better to look in a dictionary than on the Internet.