Anagrammatic quotients of free groups
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.04517
 Bibcode:
 2021arXiv211104517S
 Keywords:

 Mathematics  Group Theory;
 Computer Science  Computation and Language
 EPrint:
 14 pages, 7 of which are a long table of anagrams. Comments very welcome!