Jordan-Holder Theorem for profinite groups and applications
Group Theory
2025-03-13 v1
Abstract
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 Galois Theorem for infinite prosolvable extensions. In addition, we investigate the connection between the abstract and topological composition factors of a nonstrongly complete profinite group.
Cite
@article{arxiv.2503.09177,
title = {Jordan-Holder Theorem for profinite groups and applications},
author = {Tamar Bar-On and Nikolay Nikolov},
journal= {arXiv preprint arXiv:2503.09177},
year = {2025}
}