The paper in question is bilingual; the proof that the English homophony group is trivial is given in French, and the proof that the French homophony group is trivial is given in English. I particularly like the acknowledgements:
The third and fourth authors were partially supported by NSF and (by the results of this paper) numerous other government agencies.
A related problem is as follows: consider the group on twenty-six letters A, B, ..., Z with the relations that two words are equivalent if they are permutations of each other and each appears as a word in some dictionary of choice. Identify the center of the group. According to Steven E. Landsburg, "The Jimmy's Book", The American Mathematical Monthly, Vol. 93, No. 8 (Oct., 1986), pp. 636-638, much work was done on this problem at Chicago in the seventies.
To get started: post = pots = stop = opts = spot = tops. Since post = pots, s and t commute; since pots = opts, o and p commute. This is clearly much harder than the homophony group problem. By the way, elation = toenail. (I've been playing lots of Scrabble recently; that set of seven letters seems to come up a lot.)