Finite Groups with Given Systems of Conditionally Seminormal Subgroups

The subgroups and are said to be cc-permutable, if permutes with for some . A subgroup of a finite group is called conditionally seminormal subgroup of , if there exists a subgroup of such that and is cc-permutable with all subgroups of . In this paper, we proved that saturated formation containing...

Full description

Saved in:
Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 12; pp. 6624 - 6632
Main Author Trofimuk, A. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Geometry
Group theory
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Subgroups
supersoluble group
2010 Mathematics Subject Classification: 20D10, 20D20
saturated formation
conditionally seminormal subgroup
Sylow subgroup
maximal subgroup
Online AccessGet full text

Cover

More Information
Summary:The subgroups and are said to be cc-permutable, if permutes with for some . A subgroup of a finite group is called conditionally seminormal subgroup of , if there exists a subgroup of such that and is cc-permutable with all subgroups of . In this paper, we proved that saturated formation containing the class of all supersoluble groups is closed under product of conditionally seminormal -subgroups and with nilpotent derived subgroup or . In addition, we studied the structure of a group with given systems of conditionally seminormal subgroups.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224605186