Products of F(G)-subnormal subgroups of finite groups

A subgroup H of a finite group G is called F*( G )-subnormal if H is subnormal in H F*( G ). We show that if a group Gis a product of two F*( G )-subnormal quasinilpotent subgroups, then G is quasinilpotent. We also study groups G = AB , where A is a nilpotent F*( G )-subnormal subgroup and B is a F...

Full description

Saved in:
Bibliographic Details
Published inRussian mathematics Vol. 61; no. 6; pp. 66 - 71
Main Author Murashka, V. I.
Format Journal Article
LanguageEnglish
Published New York Allerton Press 01.06.2017
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Subgroups
finite group
subnormal subgroup
quasinilpotent group
product of subgroups
F
supersoluble group
nilpotent group
Online AccessGet full text

Cover

More Information
Summary:A subgroup H of a finite group G is called F*( G )-subnormal if H is subnormal in H F*( G ). We show that if a group Gis a product of two F*( G )-subnormal quasinilpotent subgroups, then G is quasinilpotent. We also study groups G = AB , where A is a nilpotent F*( G )-subnormal subgroup and B is a F*( G )-subnormal supersoluble subgroup. Particularly, we show that such groups G are soluble.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X17060093