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Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
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Search options not deleted user 117282
5 votes
1 answer
292 views

Words which are not inverted by any endomorphism

Let $w$ be a word in a free group $F_2$ of two generators $x_1, x_2$ such that there does not exist any endomorphism of free group which takes $w$ to $w^{-1}$. Let $w_1, w_2$ be two words in the same …
Shri's user avatar
  • 355
2 votes
0 answers
110 views

Test words in free profinite groups

Let $G$ be a group. An element $g \in G$ is said to be a test element if any endomorphism $\phi$ of $G$ such that $\phi(g) = g$ is an automorphism. The free group $F_2$ of rank $2$ is generated by $x_ …
Shri's user avatar
  • 355