Finite Groups with Systems of Generalized Normal Subgroups

Let  be a finite group and let be the lattice of all subnormal subgroups of  . Let  and  be subgroups of  and let be a sublattice in  ; i.e., , for all . Then: is the -closure of  in  ; i.e., the intersection of all subgroups in which includes  and is the -core of  in  , i.e., the subgroup in genera...

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Bibliographic Details
Published in:Siberian mathematical journal 2024-07, Vol.65 (4), p.793-803
Main Authors: Liu, A.-M., Wang, S., Safonov, V. G., Skiba, A. N.
Format: Article
Language:English
Subjects:
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Subgroups
Citations: Items that this one cites
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Summary:Let  be a finite group and let be the lattice of all subnormal subgroups of  . Let  and  be subgroups of  and let be a sublattice in  ; i.e., , for all . Then: is the -closure of  in  ; i.e., the intersection of all subgroups in which includes  and is the -core of  in  , i.e., the subgroup in generated by all subgroups of  belonging to  . A subgroup is an - -subgroup in if either or and  avoids each composition factor of between and ; i.e., . Using these notions, we give some new characterizations of soluble and supersoluble subgroups and generalize a few available results.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624040062