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Results tagged with free-groups
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user 6503
5
votes
Accepted
Units of the group algebra of a free group
A group $G$ is locally indicable if every nontrivial finitely generated subgroup surjects onto the infinite cyclic group $\mathbb{Z}$.
The following theorem was proven by Higman in 1940 [1]:
Theorem. …
- 2,821
4
votes
Words which are not inverted by any endomorphism
This partial answer just covers the case of $\psi$ non-surjective, i.e. not an automorphism.
Just to set some notation: Define $A=\langle w_1, w_2\rangle=\operatorname{im}(\phi)\leq F_2$. We will show …
- 2,821