Finite groups with Hall subnormally embedded Schmidt subgroups

A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup...

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Bibliographic Details
Published in:Communications in algebra 2020-02, Vol.48 (2), p.668-675
Main Authors: Monakhov, Victor S., Kniahina, Viktoryia N.
Format: Article
Language:English
Subjects:
Derived subgroup
finite group
Hall subgroup
nilpotent subgroup
Subgroups
subnormal subgroup
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Summary:A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2019.1654495