Abstract
A subgroup [Formula: see text] of a finite group [Formula: see text] is said to be [Formula: see text]-subgroup of [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is [Formula: see text]-quasinormal in [Formula: see text]. In this paper, we investigate the [Formula: see text]-nilpotency of the finite groups under the assumption that there is a subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and every subgroup of [Formula: see text] with order [Formula: see text] or [Formula: see text] (whenever [Formula: see text]) is [Formula: see text]-subgroup, where [Formula: see text] is a prime dividing the order of [Formula: see text] and [Formula: see text] is a Sylow [Formula: see text]-subgroup of [Formula: see text]. As an application of the results, a related problem posed by Heliel et al. in [Finite groups with minimal CSS-subgroups, Eur. J. Pure Appl. Math. 14 (2021) 1002–1014] is solved.
Sign-in/Register to access full text options 
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.
