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On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory.

Authors :
Murashka, V. I.
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]

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