A subgroup H of a finite group G is said to
be Hall normally embedded in G if there is a normal subgroup N
of G such that H is a Hall subgroup of N. A Schmidt group is a
non-nilpotent finite group whose all proper subgroups are nilpotent.
In this paper, we prove that if each Schmidt subgroup of a finite
group G is Hall normally embedded in G, then the derived subgroup
of G is nilpotent.
Description:
Kniahina V. N. On finite groups with Hall normally embedded Schmidt subgroups / V. N. Kniahina , V. S. Monakhov // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp. 90-96
Kurdachenko, L. A.; Subbotin, I. Ya.(Луганский национальный университет им. Т. Шевченко, 2005)
Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is
proven that a subgroup H of a radical ...
Koruoğlu, Ö .; Meral, T.; Sahin, R.(ДЗ "ЛНУ імені Тараса Шевченка", 2019)
Let p, q > 2 be relatively prime integers and
let Hp,q be the generalized Hecke group associated to p and q. The
generalized Hecke group Hp,q is generated by X(z) = −(z − λp)−1
and Y (z) = −(z + λq) −1 where λp = 2 cos ...
