Abstract
In this note we show that a maximal subgroup of a finite solvable group has prime index if and only if it admits a cyclic supplement which permutes with one of its Sylow systems. In particular, a finite solvable group is supersolvable if and only if each maximal subgroup admits a cyclic supplement which permutes with a Sylow system of the maximal subgroup.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
