4 papers
Jordan-Holder Theorem for profinite groups and applications
Tamar Bar-On, Nikolay Nikolov
We generalize the notions of composition series and composition factors for profinite groups, and prove a profinite version of the Jordan-Holder Theorem. We apply this to prove a G…
Krull-Schmidt Theorem for small profinite groups
Tamar Bar-On, Nikolay Nikolov
We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomor…
Groups of profinite type and profinite rigidity
Tamar Bar-On, Nikolay Nikolov
We say that a group is of \textit{profinite type} if it can be realized as a Galois group of some field extension. Using Krull's theory, this is equivalent to the ability of $G…
On the finite images of finitely generated perfect groups
Nikolay Nikolov
Let be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite -generated perfect groups. We prove a sp…