Anagrammatic quotients of free groups

Publication date: 8 November 2021

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.

Has companion code repository: https://github.com/ericstubley/anagrammatic-groups

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