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On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory.
- Source :
-
Mathematical Notes . Dec2022, Vol. 112 Issue 5/6, p932-939. 8p. - Publication Year :
- 2022
-
Abstract
- A chief factor of a group is said to be -central if . In 1997, Shemetkov posed the problem of describing finite group formations such that coincides with the class of groups for which all chief factors are -central. We refer to such formations as centrally saturated. We prove that the centrally saturated formations form a complete distributive lattice. As an answer to a question posed by Ballester-Bolinches and Perez-Ramos, conditions for a centrally saturated formation to be saturated and solvably saturated in the class of all groups are found. As a consequence, a criterion for hereditary Fitting formations to be solvably saturated is obtained. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE groups
*GROUP theory
*GROUP formation
*DISTRIBUTIVE lattices
Subjects
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 112
- Issue :
- 5/6
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 161077307
- Full Text :
- https://doi.org/10.1134/S000143462211027X