Anagrammatic quotients of free groups
This work addresses a theoretical problem in group theory and combinatorics, specifically for researchers in abstract algebra and mathematical linguistics, but it is incremental as it builds on known concepts of free groups and anagrams.
The authors determined the structure of the quotient of the free group on 26 generators by English language anagrams, finding it has a simple presentation with 301 of 325 possible commutators missing, specifically those involving letters j, q, x, or z. They developed an algorithm to compute this group for any dictionary and provided examples from the SOWPODS scrabble dictionary to verify the 301 commutators.
We determine the structure of the quotient of the free group on 26 generators by English language anagrams. This group admits a surprisingly simple presentation as a quotient of the free group by 301 of the possible 325 commutators of pairs of generators; all of the 24 missing commutators involve at least one of the letters j, q, x, z. We describe the algorithm which can be used to determine this group given any dictionary, and provide examples from the SOWPODS scrabble dictionary witnessing the 301 commutators found.