at sight of short range of time, let us talk!
If then , where
For , let us write some elements:
word length : words
Note that for odd-length-words, like we have: ,
but for even-length-words, like , we have: .
So, this group has an infinite many elements of order two and the even-length words
form a subgroup, , isomorphic to the group of the integers, and its index is .
Now the group .
Its presentation is
Words like , where is a word that begins in and ends in also, form a subgroup:
Sample of word algebra of operators