- https://doi.org/10.1080/00927872.2023.2239352
Profinite groups with abelian Sylow subgroups
- Aug 7, 2023
- Communications in Algebra
- Lucas C Lopes +2 more
Abstract
We extend the definition of a finite -group to profinite groups and give a description of profinite -groups as a triple semidirect product of two prosoluble groups with a semisimple group, extending an old result of A. M. Broshi to the profinite case. We also prove that a profinite -group with finitely generated non-trivial Fitting subgroup is metabelian-by-(finite exponent). If, in addition, G is finitely generated then it is virtually metabelian polycyclic. Communicated by Mandi Schaeffer Fry
- # Abelian Sylow Subgroups
- # Prosoluble Groups
- # Profinite Groups
- # Finite Exponent
- # Semisimple Group
- # Non-trivial Subgroup
- # Abelian Subgroups
- # Triple Product
- # Abelian Sylow
- # Fitting Subgroup