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.
翻译:我们用英文方言方言确定了26个发电机上自由组的商数结构。该组承认一个出乎意料的简单表述为自由组的商数,由325个可能的发电机配对通勤器中的301个作为自由组的商数;所有24个缺失的通勤器至少涉及1个字母j、q、x、z。我们描述了根据任何字典可以用来确定该组的算法,并提供SOWPODS编织词典中的例子,见证找到的301个通勤器。